Iain Beaton

activity

20172026

most citedOn the Unimodality of Domination Polynomials

1 citations · 2 across the 14 of their papers we have counts for

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3 papers · 1 filter

math.CO2026

Obstructions to $k$ -colouring $H$ -free graphs

Iain Beaton, Ben Cameron, Adam van Omme

A graph is $H$ -free if it has no induced subgraph isomorphic to $H$ . In 2020, Chudnovsky, Goedgebeur, Schaudt, and Zhong characterized all graphs $H$ such that there are only finit…

math.CO2026

A dichotomy for the number of vertex-critical ( $P_{5}$ , $H$ )-free graphs when $H$ is bipartite

Iain Beaton, Ben Cameron

A graph $G$ is $k$ -vertex-critical if $χ (G) = k$ , but $χ (H) < k$ for every induced subgraph $H$ of $G$ . A graph $G$ is $(H_{1}, H_{2}, \dots, H_{m})$ -free if does not contain $H_{i}$ as an induce…

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 $χ (G) = k$ but $χ (G - v) < k$ for all $v \in V (G)$ . In this paper we make progress on the open problem of the finiteness of $k$ -vertex-critical $(P_4…

Obstructions to k-colouring H-free graphs

A dichotomy for the number of vertex-critical (P5​, H)-free graphs when H is bipartite

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

Obstructions to $k$ -colouring $H$ -free graphs

A dichotomy for the number of vertex-critical ( $P_{5}$ , $H$ )-free graphs when $H$ is bipartite

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