Zobrazeno 1 - 10
of 20
pro vyhledávání: '"Nurse, Kathryn"'
We say that a signed graph is $k$-critical if it is not $k$-colorable but every one of its proper subgraphs is $k$-colorable. Using the definition of colorability due to Naserasr, Wang, and Zhu that extends the notion of circular colorability, we pro
Externí odkaz:
http://arxiv.org/abs/2309.04450
In 1983, Bouchet proved that every bidirected graph with a nowhere-zero integer-flow has a nowhere-zero 216-flow, and conjectured that 216 could be replaced with 6. This paper shows that for cyclically 5-edge-connected bidirected graphs that number c
Externí odkaz:
http://arxiv.org/abs/2309.00704
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 strengthening some of these results, we consider the \emph{balanced ch
Externí odkaz:
http://arxiv.org/abs/2308.01242
Autor:
DeVos, Matt, Nurse, Kathryn
We give a compact variation of Seymour's proof that every $2$-edge-connected graph has a nowhere-zero $\mathbb{Z}_2 \times \mathbb{Z}_3$-flow.
Comment: 2 pages
Comment: 2 pages
Externí odkaz:
http://arxiv.org/abs/2307.04768
Autor:
DeVos, Matt, Nurse, Kathryn
We give a characterization of when a signed graph $G$ with a pair of distinguished edges $e_1, e_2 \in E(G)$ has the property that all cycles containing both $e_1$ and $e_2$ have the same sign. This answers a question of Zaslavsky.
Comment: 11 p
Comment: 11 p
Externí odkaz:
http://arxiv.org/abs/2306.05574
Jaeger, Linial, Payan, and Tarsi introduced the notion of $A$-connectivity for graphs in 1992, and proved a decomposition for cubic graphs from which $A$-connectivity follows for all 3-edge-connected graphs when $|A|\geq 6$. The concept of $A$-connec
Externí odkaz:
http://arxiv.org/abs/2306.04151
In 1981 Seymour proved his famous 6-flow theorem asserting that every 2-edge-connected graph has a nowhere-zero flow in the group ${\mathbb Z}_2 \times {\mathbb Z}_3$ (in fact, he offers two proofs of this result). In this note we give a new short pr
Externí odkaz:
http://arxiv.org/abs/2302.08625
Autor:
DeVos, Matt, Nurse, Kathryn
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 which however one seeks maximum and not minimum; this problem known as th
Externí odkaz:
http://arxiv.org/abs/1810.12277
Publikováno v:
Journal of Graph Theory; Sep2024, Vol. 107 Issue 1, p212-239, 28p
Publikováno v:
Journal of Graph Theory; Oct2024, Vol. 106 Issue 4, p944-946, 3p