Jessica McDonald

activity

20242026

collaborators

12 papers

math.CO2026

Towards the Overfull Conjecture II

Guantao Chen, Jessica McDonald, Songling Shan

Let $G$ be a simple graph with maximum degree $I^ (G)$ . A subgraph $H \subseteq G$ is $I^ (G)$ -overfull if $∣ E (H) ∣ > I^ (G) ⌊ ∣ V (H) ∣/2 ⌋$ . In any edge coloring of $G…

math.CO2026

Coloring graphs with independence number two and no odd clique immersions

Henry EcheverrÃa, Jessica McDonald

We study the chromatic number of graphs that exclude a clique as a strong odd immersion and have independence number two. Given a graph $G$ and $t \in Z^{+}$ , we prove that if…

math.CO2026

On graphs with girth at least five achieving Steffen's edge coloring bound

Guantao Chen, Alireza Fiujlaali, Anna Johnsen-Yu +1

Vizing and Gupta showed that the chromatic index $I ¨ ^{'} (G)$ of a graph $G$ is bounded above by $I^ (G) + I^¼ (G)$ , where $I^ (G)$ and $I^¼ (G)$ denote the maximum degree and the maximum mu…

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.CO2025

Extending total colorings in planar graphs

Owen Henderschedt, Jessica McDonald

We initiate the study of total-coloring extensions, and focus our attention on planar graphs, asking: ``When can a total- $k$ -coloring of some subgraph $H$ of a planar graph $G$ be…

math.CO2025

Cliques and High Odd Holes in Graphs with Chromatic Number Equal to Maximum Degree

Rachel Galindo, Jessica McDonald, Songling Shan

We give a uniform and self-contained proof that if $G$ is a connected graph with $I ¨ (G) = I^ (G)$ and $G \neq = C_{7}$ , then $G$ contains either $K_{I^ (G)}$ or an odd hole whe…