Kathryn Nurse

collaborators

5 papers

math.CO2023

Density of $3$ -critical signed graphs

Laurent Beaudou, Penny Haxell, Kathryn Nurse +2

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,…

math.CO2023

Nowhere-zero 8-flows in cyclically 5-edge-connected, flow-admissible signed graphs

Matt DeVos, Kathryn Nurse, Robert Sámal

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 show…

math.CO2023

Cycles through two edges in signed graphs

Matt DeVos, Kathryn Nurse

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 t…

math.CO2023

Group connectivity of 3-edge-connected signed graphs

Alejandra Brewer Castano, Jessica McDonald, Kathryn Nurse

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 a…

math.CO2023

Another proof of Seymour's 6-flow theorem

Matt DeVos, Jessica McDonald, Kathryn Nurse

In 1981 Seymour proved his famous 6-flow theorem asserting that every 2-edge-connected graph has a nowhere-zero flow in the group $Z_{2} \times Z_{3}$ (in fact, he…

Density of 3-critical signed graphs

Nowhere-zero 8-flows in cyclically 5-edge-connected, flow-admissible signed graphs

Cycles through two edges in signed graphs

Group connectivity of 3-edge-connected signed graphs

Another proof of Seymour's 6-flow theorem

Density of $3$ -critical signed graphs