Jessica McDonald

activity

20112026

most citedMinimum degree condition forcing complete graph immersion

8 citations · 8 across the 7 of their papers we have counts for

collaborators

6 papers

math.CO2025

Degree sequences realizing labelled perfect matchings

Joseph Briggs, Jessica McDonald, Songling Shan

Let $n \in N$ and $d_{1} \geq d_{2} \geq d_{n} \geq 1$ be integers. There is characterization of when $(d_{1}, d_{1}, \dots, d_{n})$ is the degree sequence of a graph containing a perf…

math.CO2024

On graphs with chromatic number and maximum degree both equal to nine

Rachel Galindo, Jessica McDonald

An equivalent version of the Borodin-Kostochka Conjecture, due to Cranston and Rabern, says that any graph with $χ = Δ = 9$ contains $K_{3} \lor E_{6}$ as a subgraph. Here we prove sever…

math.CO2024

A reduction of the "cycles plus $K_{4}$ 's" problem

Aseem Dalal, Jessica McDonald, Songling Shan

Let $H$ be a 2-regular graph and let $G$ be obtained from $H$ by gluing in vertex-disjoint copies of $K_{4}$ . The "cycles plus $K_{4}$ 's" problem is to show that $G$ is 4-colourable; 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…

math.CO2011★ 8 cited

Minimum degree condition forcing complete graph immersion

Matt DeVos, Zdeněk Dvořák, Jacob Fox +3

An immersion of a graph $H$ into a graph $G$ is a one-to-one mapping $f : V (H) \to V (G)$ and a collection of edge-disjoint paths in $G$ , one for each edge of $H$ , such that the path…