Ben Cameron

activity

20242026

collaborators

4 papers

math.CO2026

Vertex-critical graphs in subfamilies of $(P_{4} + ℓ P_{1})$ -free graphs

Iain Beaton, Ben Cameron

A graph $G$ is $k$ -vertex-critical if $I ¨ (G) = k$ but $I ¨ (G - v) < k$ for all $v \in V (G)$ . In this paper we make progress on the open problem of the finiteness of $k$ -vertex-critical $(P…

math.CO2025

On GyÃ¡rfÃ¡s' Path-Colour Problem

Ben Cameron, Alexander Clow

In their 1997 paper titled ``Fruit Salad", GyÃ¡rfÃ¡s posed the following conjecture: there exists a constant $k$ such that if each path of a graph spans a $3$ -colourable subgraph,…

math.CO2025

Critical $(P_{5}, W_{4})$ -Free Graphs

Wen Xia, Jorik Jooken, Jan Goedgebeur +3

A graph $G$ is $k$ -vertex-critical if $I ¨ (G) = k$ but $I ¨ (G - v) < k$ for all $v \in V (G)$ . A graph is $(H_{1}, H_{2})$ -free if it contains no induced subgraph isomorphic to $H_{1}$ nor $H_{2}$ …

math.CO2024

Vertex-critical graphs in co-gem-free graphs

Iain Beaton, Ben Cameron

A graph $G$ is $k$ -vertex-critical if $I ¨ (G) = k$ but $I ¨ (G - v) < k$ for all $v \in V (G)$ and $(G, H)$ -free if it contains no induced subgraph isomorphic to $G$ or $H$ . We show that there…

Vertex-critical graphs in subfamilies of (P4​+ℓP1​)-free graphs

On GyÃ¡rfÃ¡s' Path-Colour Problem

Critical (P5​,W4​)-Free Graphs

Vertex-critical graphs in co-gem-free graphs

Vertex-critical graphs in subfamilies of $(P_{4} + ℓ P_{1})$ -free graphs

Critical $(P_{5}, W_{4})$ -Free Graphs