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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Showing 2024Show all

3 papers · 1 filter

math.CO2024

Reconfiguration graphs for minimal domination sets

Iain Beaton

A dominating set $S$ in a graph is a subset of vertices such that every vertex is either in $S$ or adjacent to a vertex in $S$ . A minimal dominating set $M$ is a dominating set suc…

math.CO2024

On the unimodality of nearly well-dominated trees

Iain Beaton, Sam Schoonhoven

A polynomial is said to be unimodal if its coefficients are non-decreasing and then non-increasing. The domination polynomial of a graph $G$ is the generating function of the numbe…

math.CO2024

Vertex-critical graphs in co-gem-free graphs

Iain Beaton, Ben Cameron

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