The project 'Packing, covering and partitions of digraphs' is funded by the DKK 2,592,000 grant DFF-7014-00037A from the Independent Research Fund Denmark, Natural Sciences, running from January 1, 2018 through December 31, 2023. | |

The project is carried out at the Department of Mathematics and Computer Science (IMADA) at the University of Southern Denmark. |

## Participants

- Jørgen Bang-Jensen (PI)
- Anders Yeo
- Marco Chiarandini (until December 2018)
- Thomas Bellitto (From August 2018 to February 2020 as a Post Doc)
- Tilde My Christiansen (PhD student until December 2018)
- Kristine Vitting Klinkby Knudsen (PhD student until August 2021). Kristine continued in the project as a postdoc until December 2022.
- Yun Wang (PhD student from December 1, 2021 till November 30, 2023.

## Environment

The project is carried out at the Department of Mathematics and Computer Science (IMADA) at the University of Southern Denmark. The participants are all associated with the Research Training Programs in Mathematics and Computer Science as Ph.D. advisors.## Activities

Besides supervision of one postdoc, Thomas Bellitto, who was hired for 18 months starting in August 2018, the activities on this grant are research related traveling to conferences, meetings by invitation, research collaboration, and hosting guests.

### Research visits and other external activities by members of the grant

## 2018

- January 2018: Bang-Jensen visited LIRMM, Universite Montpellier for two weeks to work with Stephane Bessy
- May 2018: Bang-Jensen visited LIRMM, Universite Montpellier for two weeks to work with Stephane Bessy.
- June 2018: Bang-Jensen visited INRIA project team Coati for one week to work with Frederic Havet
- June 11-15, 2018: Bang-Jensen participated in SGT2018 in SETE, France.
- June 26-29, 2018: Bang-Jensen participated in DMD2018 in Sevilla, Spain.
- July 8-11, 2018: Marco Chiarandini participated in EURO 2018 in Valencia Spain. Marco gave a talk entitled 'Course Timetabling in a Flexible Semester Structure'
- August 4-10, 2018: Bang-Jensen visited Simon Fraser University, Burnaby B.C., Canada to work with Pavol Hell.
- August 10-19, 2018: Bang-Jensen visited University of Victoria, Victoria BC, Canada to work with Jing Huang.
- August 26-28, 2018: Bang-Jensen visited LABRI, Universite Bordeaux, France as a member of the PhD committee of Thomas Bellitto.

## 2019

- January 7-12, 2019 Bang-Jensen visited INRIA project team Coati to work with Frederic Havet.
- January 12-18, 2019 Bang-Jensen visited LIRMM, Universite Montpellier for two weeks to work with Stephane Bessy.
- May 21-25, 2019 Bang-Jensen visited LIRMM, Universite Montpellier to work with Stephane Bessy.
- May 25-29, 2019 Bang-Jensen visited INRIA project team Coati to work with Frederic Havet.
- May 28-31, 2019 Bellitto attended CanaDAM 2019 in Vancouver and gave the talk 'Connecting edge-colouring'.
- May 31-June 16 Bellito visited Department of Mathematics and Statistics at University of Victoria to work with Gary MacGillivray.
- June 24-28, 2019: Bellitto attended "Structural graph theory workshop at Gułtowy, Poland"
- August 5-7, 2019: Bang-Jensen, Bellitto and Yeo participated in Norcom 2019 at Schaeffergaarden in Gentofte. Bang-Jensen gave the talk "Good acyclic orientations, antistrong digraphs and matroids" and Yeo gave the talk "Spanning eulerian subdigraphs avoiding k prescribed arcs in tournaments"
- August 25-September 2, 2019: Bang-Jensen visited, LIRMM, Universite Montpellier to work with Stephane Bessy and Dieter Rautenbach
- October 28-31, 2019, Bellitto attended the conference BGW 2019 in Bordeaux and gave the talk: “Connecting edge-colouring”
- November 13-15, 2019, Bellitto attended the conference JGA 2019 in Brussels and gave the talk: Hajós construction for digraphs”
- November 18-21, 2019, Yeo visited LIRMM Universite Montpellier to work with Stephane Bessy and as an external evaluator on the PhD thesis of Jocelyn Thiebaut

## 2020

Due to Covid-19 most of our travelplans had to be cancelled.- February 1-5, 2020 and February 11-20, 2020: Bang-Jensen visited INRIA project team Coati to work with Frederic Havet.
- February 5-11, 2020: Bang-Jensen visited LIRMM, Universite Montpellier to work with Stephane Bessy.
- February 25- June 10, 2020: Bang-Jensen visited INRIA project team Coati to work with Frederic Havet and others at INRIA. Unfortunately this part was heavily affected by Covid-19.

## 2021

Again due to the Covid-19 situation we have had very little travel.- August 20-27, 2021: Bang-Jensen visited LIRMM, Universite Montpellier to work with Stephane Bessy, Daniel Goncalves and Lucas Piccassari.
- September 10, 2021: Bang-Jensen acted as the external opponent on the PhD thesis of Jonas Granholm at Linkoping University, Sweden.

## 2022

- June 30-July 15 Bang-Jensen visited LIRMM, Université Montpellier. July 4-8 he attended ICGT 2022 in Montpellier. He gave the talk ’Making a tournament k-strong by adding new arcs’. This is based on joint work with Anders Yeo and former Masters student Kasper Skov Johansen, now a research assistant at DTU Compute. Kasper will start his PhD studies at DTU later this fall. At ICGT Bang-Jensen also chaired the opening plenary talk by Reinhard Diestel. While in Montpellier, Bang-Jensen also visited his research collaborator Stephane Bessy at LIRMM Université Montpellier https://www.lirmm.fr/~bessy/ They continued their long term collaboration on the structure of directed graphs.
- July 3-July 9: Yun Wang attended ICGT 2022 in Montpellier. She gave the talk "Arc-disjoint in and out-branchings in co-bipartite digraphs"
- October 5-October 11: Bang-Jensen visited LRI, Universite Paris-Sud. On October 10 he was a main speaker at the one day meeting in the memory of Yannis Manoussakis. The topic of the talk was connections between digraphs and edge-coloured graphs.

## 2023

- May 16-May 28 Bang-Jensen visited team Coati, INRIA Sophia Antipolis to work with Lucas Picasarri-Arietta.
- May 29-June 4 Bang-Jensen attended the ANR Digraphs workshop in Sete, France and gave the invited lecture "Open problems on digraphs".
- July 29-August 16 Bang-Jensen visited Department of Mathematics and Statistics, University of Victoria to work with Jing Huang.

### Visits by collaborators

## 2018

- April 3-September 30, 2018: Michael Stiebitz, Department of Mathematics, Technische Universitat Ilmenau, visited us at SDU for 6 months.
- April 8-13,2018: Frederic Havet, INRIA, Sophia Antipolis visited us for one week at SDU and gave the talk 'Identifying codes in grids'.
- August 20-24, 2018: Stephane Bessy, LIRMM Universite Montpellier, France visited us at SDU.
- August 20-September 2nd: Mike Henning, University of Johannesburg, South Africa visited us at SDU.
- September 16-22, 2018: Matthias Kriesell, Department of Mathematics, Technische Universitat Ilmenau, visited us at SDU and gave the talk 'Certifying High Connectivity'.
- September 15-22, 2018: Thomas Schweser, Department of Mathematics, Technische Universitat Ilmenau, visited us at SDU.
- December 2-7, 2018, William Lochet, University of Bergen, Norway visited us and gave a talk entitled 'AVD coloring and entropy compression'.
- December 14-19, 2018, Jing Huang, Department of Mathematics and Statistics, University of Victoria visited us in connection with Tilde My Christansen's PhD defense.
- December 18-21, 2018 Gregory Gutin, Royal Holloway, University of London, visited us.

## 2019

- February 1 to March 31, 2019: Michael Stiebitz, Department of Mathematics, Technische Universitat Ilmenau, visited us at SDU for 2 months.
- February 12-28, 2019: Matthias Kriesell, Department of Mathematics, Technische Universitat Ilmenau, visited us at SDU
- March 5-15, 2019: Thomas Schweser, Department of Mathematics, Technische Universitat Ilmenau, visited us at SDU.
- May 3-July 15, 2019: Hugues Depres, ENS Lyon visited the group as part of his internship program at ENS.
- June 10-14, 2019: Stephane Bessy, LIRMM Universite Montpellier, France visited us at SDU.
- August 7-16, 2019: Kathie Cameron, Wilfried Laurier University, Canada visited us at SDU
- August 7-16, 2019: The world famous Jack Edmonds, Canada, one of the fathers of combinatorial optimization visited us at SDU.
- September 23-27, 2019, Mike Henning, University of Johannesburg, South Africa visited us at SDU and gave the talk: Matching and edge-connectivity in graphs with given maximum degree
- September 18-October 3, 2019, Matthias Kriesell, Department of Mathematics, Technische Universitat Ilmenau, visited us at SDU

## 2020

Due to Covid-19 most of our planned visitors had to cancel their visit.- July-September 2020: Michael Stiebitz, Department of Mathematics, Technische Universitat Ilmenau, visited us at SDU for 3 months.
- July 2020: Thomas Schweser, Department of Mathematics, Technische Universitat Ilmenau, visited us for one week at SDU.
- September 2020: Thomas Schweser, Department of Mathematics, Technische Universitat Ilmenau, visited us for weeks at SDU.
- September 27-October 3, 2020 Stephane Bessy, LIRMM Universite Montpellier, France visited us at SDU.

## 2021

Due to Covid-19 most of our planned visitors had to be canceled- July-September 2021: Michael Stiebitz, Department of Mathematics, Technische Universitat Ilmenau, visited us at SDU for 3 months.
- July 2020: Thomas Schweser, Department of Mathematics, Technische Universitat Ilmenau, visited us for 3 weeks at SDU.

## 2022

- July-September 2022: Michael Stiebitz, Department of Mathematics, Technische Universitat Ilmenau, visited u\ s at SDU for 3 months.
- August 21-26 2022: Yubao Guo, RWTH Aachen, visited us and gave the talk: Extensions of Moon's and Alspach's theorems on tournaments to multipartite tournaments.
- August 28-September 3 2022: Florian Hörsch, TU-Ilmenau, visited us and gave the talk: Orientations and connectivity.

## 2023

- January 15-20: Florian Hörsch, TU-Ilmenau, visited us.
- June-August: Michael Stiebitz, Department of Mathematics, Technische Universitat Ilmenau, visited us for 3 months.
- September 20- October 1: Michael Stiebitz, Department of Mathematics, Technische Universitat Ilmenau, September 24-October 1, Lucas Picasarri-Arietta, INRIA, Sophia Antipolis, France visited us.
- August 29-September 1, 2018: Bang-Jensen and his college Bjarne Toft organized the conference GT2018 at Hotel Storebælt in Nyborg
- December 17, 2018: Tilde My Christiansen successfully defended her PhD thesis, Algorithmic and structural problems in digraphs.
- July 6-10, 2020: Bang-Jensen gave a 30 hour course on Directed graphs as part of the summerschool on Graph theory at Shandong University in China link to info about the course
- March 17-18, 2021: Bang-Jensen gave two online presentations on good acyclic orientations of graphs to researchers at Shandong University in China.
- November 26, 2021: Kristine Vitting Klinkby Knudsen succesfully defended her PhD Thesis, Parameterized problems on (Di)graphs. She will receive a cotutelle PhD degree from University of Bergen and University of Southern Denmark.
- July 3-7, 2023: Bang-Jensen gave a 30 hour online course on Directed graphs as part of the summerschool\ on Graph theory at Shandong University in China
**Classes of Directed Graphs.**- Jørgen Bang-Jensen, Gregory Gutin (editors)
*Springer Monographs in Mathematics, 2018.* **Basic Terminology, Notation and Results.**- Jørgen Bang-Jensen, Gregory Gutin
- Chapter 1 in 'Classes of Directed Graphs', Bang-Jensen and Gutin (eds)
*Springer Monographs in Mathematics, 2018.* **Tournaments and Semicomplete digraphs.**- Jørgen Bang-Jensen, Frederic Havet
- Chapter 2 in 'Classes of Directed Graphs', Bang-Jensen and Gutin (eds)
*Springer Monographs in Mathematics, 2018.* **Locally Semicomplete digraphs and Generalizations.**- Jørgen Bang-Jensen
*Chapter 6 in 'Classes of Directed Graphs', Bang-Jensen and Gutin (eds)**Springer Monographs in Mathematics, 2018.* **Semicomplete Multipartite Digraphs.**- Anders Yeo
*Chapter 7 in 'Classes of Directed Graphs', Bang-Jensen and Gutin (eds)**Springer Monographs in Mathematics, 2018.* **Not-all-equal 3-SAT and 2-colorings of 4-regular 4-uniform hypergraphs.**- Michael A. Henning, Anders Yeo:
*Discrete Mathematics 341(8): 2285-2292 (2018)* **Degree constrained 2-partitions of semicomplete digraphs.**- Jørgen Bang-Jensen, Tilde My Christiansen
*Theoretical Computer Science*746: 112-123 (2018) **Out-degree reducing partitions of digraphs.**- Jørgen Bang-Jensen, Stéphane Bessy, Frédéric Havet, Anders Yeo.
*Theoretical Computer Science*719: 64-72, 2018.

**Chi-bounded families of oriented graphs.**- Pierre Aboulker, Jørgen Bang-Jensen, Nicolas Bousquet, Pierre Charbit, Frédéric Havet, Frédéric Maffray, José Zamora.
*Journal of Graph Theory*87: 285-304 (2018).

**Completing orientations of partially oriented graphs.**- Jørgen Bang-Jensen, Jing Huang, Xuding Zhu.
*Journal of Graph Theory*87: 285-304, 2018.

**Bipartite spanning sub(di)graphs induced by 2-partitions.**- Jørgen Bang-Jensen, Stéphane Bessy, Frédéric Havet, Anders Yeo.
*Journal of Graph Theory*89: 304-326, 2018.

**Tight lower bounds on the matching number in a graph with given maximum degree**- Michael A. Henning and Anders Yeo.
*Journal of Graph Theory*89: 115-149, 2018.

**On upper transversals in 3-uniform hypergraphs**- Michael A. Henning and Anders Yeo.
*Electronic J. Combin.*25(4): P4.27, 2018.

**Complexity of locally-injective homomorphisms to tournaments***Stefan Bard, Thomas Bellitto, Christopher Duffy, Gary MacGillivray, Feiran Yang.*20(2) (2018)

Discrete Mathematics & Theoretical Computer Science

**Upper transversals in hypergraphs**- Michael A. Henning and Anders Yeo.
*Eur. J. Comb.*78 1-12 (2019)

**Degree constrained 2-partitions of graphs.**- Jørgen Bang-Jensen, Stéphane Bessy
*Theoretical Computer Science*776: 64-74, 2019.

**Bipartite spanning sub(di)graphs induced by 2‐partitions**- Jørgen Bang-Jensen, Stéphane Bessy, Frederic Havet, Anders Yeo
*Journal of Graph Theory*92: 130-151, 2019.

**The parameterized complexity landscape of finding 2-partitions of digraphs**- Jørgen Bang-Jensen, Kristine Vitting Klinkby, Saket Saurabh, Meirav Zehavi
*Theoretical Computer Science*795: 108-114, 2019.

**Out-colourings of digraphs**- Noga Alon, Jørgen Bang-Jensen, Stéphane Bessy
*Journal of Graph Theory*93: 88-112, 2020.

**On DP-colourings of digraphs**- Jørgen Bang-Jensen, Thomas Bellitto, Thomas Schweser, Michael Stiebitz
*Journal of Graph Theory*95: 76-98, 2020.

**Hajos and Ore Constructions for Digraphs**- Jørgen Bang-Jensen, Thomas Bellitto, Thomas Schweser, Michael Stiebitz
*Electronic J. Combinatorics*27(1): P1.63, 2020.

**The directed 2-linkage problem with length constraints**- Jørgen Bang-Jensen, Thomas Bellitto, William Lochet, Anders Yeo.
*Theoretical Computer Science*814: 69-73, 2020.

**Bounds on upper transversals in hypergraphs**- Michael A. Henning, Anders Yeo
*J. Combinatorial Optimization*39(1): 77-99, 2020.

**Arc-disjoint strong spanning subdigraphs of semicomplete compositions**- Jørgen Bang-Jensen, Gregory Gutin, Anders Yeo
*Journal of Graph Theory*95(2) 267-289 2020

**Spanning eulerian subdigraphs avoiding k presecibed arcs in tournaments**- Jørgen Bang-Jensen, Hugues Depres, Anders Yeo
*Discrete Mathematics*343(12) 112129 (2020). /

**On the parametrized complexity of 2-partitions**- Jonas Bamse Andersen, Jørgen Bang-Jensen, Anders Yeo
*Theoretical Computer Science*844: 69-73 (2020)

**Proper‐walk connection number of graphs**- Jørgen Bang-Jensen, Thomas Bellitto, Anders Yeo
*Journal of Graph Theory*96(1): 137-159 (2021)

**Good orientations of unions of edge-disjoint spanning trees**- Jørgen Bang-Jensen, Stephane Bessy, Jing Huang, Matthias Kriesell
*Journal of Graph Theory*96: 594-618 2021.

**Affine Planes and Transversals in 3-Uniform Linear Hypergraphs**- Michael A. Henning, Anders Yeo
*Graphs and Combinatorics*37(3): 867-890 2021.

**Dominating vertex covers: the vertex-edge domination problem.**- William Klostermeyer, Magaret-Ellen Messinger, Anders Yeo
*Discuss. Math. Graph Theory*41(1) 123-132 2021.

**Matching and edge-connectivity in graphs with given maximum degree**- Michael A. Henning, Anders Yeo
*Discrete Math.*344(8) 112438 2021.

**On Supereulerian 2-edge coloured graphs**- Jørgen Bang-Jensen, Thomas Bellitto, Anders Yeo
*Graphs and Combinatorics*37(6) 2601-2620 2021.

**A new upper bound on the total domination number in graphs with minimum degree six**- Michael Henning, Anders Yeo
*Discrete Appl. Math.*302 1-7 2021.

**Lower bounds on Tuza constants for transversals in linear uniform hypergraphs**- Michael Henning, Anders Yeo
*Discrete Appl. Math.*304 12-22 2021.

**Component order connectivity in directed graphs**- Jørgen Bang-Jensen, Eduard Eiben, Gregory Z. Gutin, Magnus Wahlström, Anders Yeo
*Algorithmica*84(9) 2767-2784 2022.

**Every (13k - 6)-strong tournament with minimum out-degree at least 28k - 13 is k-linked**- Jørgen Bang-Jensen, Kasper Skov Johansen
*Discrete Mathematics*345(6) 112831 2022.

**Low chromatic spanning sub(di)graphs with prescribed degree or connectivity properties**- Jørgen Bang-Jensen, Frédéric Havet, Matthias Kriesell, Anders Yeo
*J. Graph Theory*99(4) 615-636 2022 .

**Arc-disjoint in- and out-branchings in digraphs of independence number at most 2.**- Jørgen Bang-Jensen, Stéphane Bessy, Frédéric Havet, Anders Yeo
*J. Graph Theory*100(2) 294-314 2022.

**Good acyclic orientations of 4-regular 4-connected graphs**- Jørgen Bang-Jensen, Matthias Kriesell
*J. Graph Theory*100(4) 698-720 2022.

**Digraphs and Variable Degeneracy**- Jørgen Bang-Jensen, Thomas Schweser, Michael Stiebitz
*Siam J. Disc. Math*36(1) 578-595 2022.

**Complexity of some arc-partition problems for digraphs**- Jørgen Bang-Jensen, Stéphane Bessy, Daniel Gonçalves, Lucas Picasarri-Arrieta
*Theoretical Computer Science*928 167-182 2022.

**Low chromatics spanning sub(di)graphs with prescribed degree or connectivity properties**- Jørgen Bang-Jensen, Fredderic Havet, matthias Kriesell, Anders Yeo
*J. Graph Theory*99 615-636 (2022).

**Non-separating spanning trees and out-branchings in digraphs of independence number 2**- Jørgen Bang-Jensen, Stéphane Bessy, Anders Yeo
*Graphs Comb.*38 187 (2022).

**Complexity of (arc)-connectivity problems involving arc-reversals or deorientations**- Jørgen Bang-Jensen, Florian Hoersch. Matthias Kriesell
*Theor. Comput. Sci.*973 114097 (2023).

**The complexity of finding low chromatic spanning sub(di)graphs with prescribed connectivity properties**- Jørgen Bang-Jensen, Anders Yeo
*Theor. Comput. Sci*949 113758 (2023).

**Spanning eulerian subdigraphs in semicomplete digraphs**- Jørgen Bang-Jensen, Frederic Havet, Anders Yeo
*J. Graph Theory*102 578-606 (2023).

**Exact capacitated domination: On the computational complexity of uniqueness**- Gregory Z. Gutin, Philip R. Neary, Anders Yeo
*Discret. Appl. Math*332 155-169 (2023).

**(1,1)-Cluster editing is polynomial-time solvable**- Gregory Z. Gutin, Anders Yeo
*Discret. Appl. Math*340 259-271 (2023).

**Results on the small quasi-kernel conjecture**- Jiangdong Ai, Stefanie Gerke, Gregory Z. Gutin, Anders Yeo, Yacong Zhou
*Discret. Math.*346 113435 (2023).

**k-best feature selection and ranking via stochastic approximation.**- David V. Akman, Milad Malekipirbazari, Zeren D. Yenice, Anders Yeo, Niranjan Adhikari, Yong Kai Wong, Babak Abbasi, Alev Taskin Gumus
*Expert Syst. Appl.*213 118864 (2023).

**Unique Stable matchings**- Gregory Z. Gutin, Philip R. Neary, Anders Yeo
*Games Econ. Behav.*141 529-457 (2023).

**Directed Steiner tree packing and directed tree connectivity**- Yuefang Sun, Anders Yeo
*J. Graph Theory**102 86-106 (2023).*

**Lower bounds for maximum weighted cut***Gregory Z. Gutin, Anders Yeo**Discret. Math.*1142-1161 (2023).

**Preference swaps for the stable matching problem***Eduard Eiben, Gregory Z. Gutin, Philip R. Neary, Clément Rambaud, Magnus Wahlström, Anders Yeo**Theor. Comput. Sci.*940 222-230 (2023).

**The Tuza-Vestergaard theorem***Michael A. Henning, Christian Löwenstein, Anders Yeo**SIAM J. Disc. Math.*37 1275-1310 (2023).### Peer-Reviewed International Conference Articles

**Parameterized Algorithms for Survivable Network Design with Uniform Demands.***Jørgen Bang-Jensen, Manu Basavaraju, Kristine Vitting Klinkby, Pranabendu Misra, M. S. Ramanujan, Saket Saurabh, Meirav Zehavi:**SODA*: 2838-2850, SIAM, 2018.

[Proceedings of the Twenty-Ninth Annual {ACM-SIAM} Symposium on Discrete Algorithms, {SODA} 2018, New Orleans, LA, USA, January 7-10, 2018.]

**Component Order Connectivity in Directed Graphs***Jørgen Bang-Jensen, Eduard Eiben, Gregory Gutin, Magnus Wahlstrom and Anders Yeo,**IPEC 2020*: 2:1-2:16 (2020)

**Inversion number of an oriented graph and related parameters***Jørgen Bang-Jensen, Jonas Costa Ferreira da Silva, Frédéric Havet**ALGOS 2020*101-121 2020.

**k-Distinct Branchings Admits a Polynomial Kernel***Jørgen Bang-Jensen, Kristine Vitting Klinkby Knudsen, Saket Saurabh,**ESA*11.1-11.15 2021.

**Strong Connectivity Augmentation is FPT***Kristine Vitting Klinkby, Pranabendu Misra, Saket Saurabh.**SODA:*219-234, SIAM, 2021.

### Meetings arranged or co-arranged by the group

### Other events

## Short Project description

The project deals with structural and algorithmic aspects of problems related to packing, coverings or partitions in digraphs and generalizations of digraphs such as edge-coloured graphs. Examples are: packing cycles, linkage problems, packing strong subdigraphs, branchings, vertex partitions with prescribed properties in (di)graphs, packing sub(di)graphs in digraphs, edge-coloured graphs, completing partial orientations of graphs to obtain digraphs with prescribed properties.## Publications

Here we list project related publications by members of the group since January 1, 2018.### Books and chapters in books

### Peer-Reviewed International Journal Articles