From the 1 of 6 linked papers with an AI index.
6 papers
Acyclic Dichromatic Number of Tournaments: these are the Champions
Pierre Aboulker, Pierre Charbit, Samuel Coulomb +2
The paper characterizes the subtournaments that must occur in any tournament with a sufficiently large acyclic dichromatic number, confirming a conjecture and establishing a local‑…
Balanced-chromatic number and Hadwiger-like conjectures
Andrea Jiménez, Jessica McDonald, Reza Naserasr +2
Motivated by different characterizations of planar graphs and the 4-Color Theorem, several structural results concerning graphs of high chromatic number have been obtained. Toward…
Bouchet's conjecture for cyclically 5-edge-connected, cubic signed graphs
Kathryn Nurse
A 1983 conjecture of Bouchet states that every flow-admissible signed graph has a nowhere-zero six-flow. We prove this conjecture for cyclically five-edge-connected, cubic signed g…
Nowhere-zero 8-flows in 3-edge-connected signed graphs
Matt DeVos, Kathryn Nurse, Robert Šámal
In 1983, A. Bouchet extended W.T. Tutte's notion of nowhere-zero flows to signed graphs, and conjectured that every flow-admissible signed graph has a nowhere-zero 6-flow. In this…
On the Ban-Linial Conjecture
Matt DeVos, Kathryn Nurse
Let be a graph and let be a partition of . This partition is called external or unfriendly if every has at least as many neighbours in …
A Maximum Linear Arrangement Problem on Directed Graphs
Matt DeVos, Kathryn Nurse
We propose a new arrangement problem on directed graphs, Maximum Directed Linear Arrangement (MaxDLA). This is a directed variant of a similar problem for undirected graphs, in whi…