Ben Cameron

activity

20222024

k

-vertex-critical (

P_{5}

C_{5}

)-free graphs

1 citations · 1 across the 4 of their papers we have counts for

collaborators

4 papers

math.CO2024

On the finiteness of $k$ -vertex-critical $2 P_{2}$ -free graphs with forbidden induced squids or bulls

Melvin Adekanye, Christopher Bury, Ben Cameron +1

A graph 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 are o…

math.CO2024

An approximation algorithm for zero forcing

Ben Cameron, Jeannette Janssen, Rogers Matthew +1

We give an algorithm that finds a zero forcing set which approximates the optimal size by a factor of $pw (G) + 1$ , where $pw (G)$ is the pathwidth of $G$ . Starting from…

math.CO2023★ 1 cited

Infinite families of $k$ -vertex-critical ( $P_{5}$ , $C_{5}$ )-free graphs

Ben Cameron, Chính T. Hoàng

A graph is $k$ -vertex-critical if $χ (G) = k$ but $χ (G - v) < k$ for all $v \in V (G)$ . We construct a new infinite families of $k$ -vertex-critical $(P_{5}, C_{5})$ -free graphs for all $k \geq 6$ .…

math.CO2022

A Tight Upper Bound on the Average Order of Dominating Sets of a Graph

Iain Beaton, Ben Cameron

In this paper we study the the average order of dominating sets in a graph, $avd (G)$ . Like other average graph parameters, the extremal graphs are of interest. Beato…

On the finiteness of k-vertex-critical 2P2​-free graphs with forbidden induced squids or bulls

An approximation algorithm for zero forcing

Infinite families of k-vertex-critical (P5​, C5​)-free graphs

A Tight Upper Bound on the Average Order of Dominating Sets of a Graph

On the finiteness of $k$ -vertex-critical $2 P_{2}$ -free graphs with forbidden induced squids or bulls

Infinite families of $k$ -vertex-critical ( $P_{5}$ , $C_{5}$ )-free graphs