Alexander Clow

activity

20212026

most citedOriented Colouring Graphs of Bounded Degree and Degeneracy

1 citations · 1 across the 13 of their papers we have counts for

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Showing 2023Show all

6 papers · 1 filter

math.CO2023

Expanders Satisfy the Weak Meyniel Conjecture

Alexander Clow

We show that if ${G_{n}}_{n \geq 1}$ is a sequence of graphs of order $n$ with bounded maximum degree and isoperimetric function $Φ (G_{n}, n^{1 - α})$ bounded away from $0$ as $n\rightar…

math.CO2023

Injective edge colorings of degenerate graphs and the oriented chromatic number

Peter Bradshaw, Alexander Clow, Jingwei Xu

Given a graph $G$ , an injective edge-coloring of $G$ is a function $ψ : E (G) \to N$ such that if $ψ (e) = ψ (e^{'})$ , then no third edge joins an endpoint of $e$ and an en…

math.CO2023

Eternal Distance-2 Domination in Trees

Alexander Clow, Christopher M van Bommel

We consider the eternal distance-2 domination problem, recently proposed by Cox, Meger, and Messinger, on trees. We show that finding a minimum eternal distance-2 dominating set of…

math.CO2023

Graphs with Large Girth and Small Cop Number

Alexander Clow

In this paper we consider the cop number of graphs with no, or few, short cycles. We show that when $G$ is graph of girth $g$ and the minimum degree $δ \geq 2$ , then $c(G) = O(n\log…

math.CO2023

Ordinal Sums of Numbers

Alexander Clow, Neil McKay

In this paper we consider ordinal sums of combinatorial games where each summand is a number, not necessarily in canonical form. In doing so we give formulas for the value of an or…

math.CO2023★ 1 cited

Oriented Colouring Graphs of Bounded Degree and Degeneracy

Alexander Clow, Ladislav Stacho

This paper considers upper bounds on the oriented chromatic number $χ_{o} (G)$ , of an oriented graph $G$ in terms of its $2$ -dipath chromatic number $χ_{2} (G)$ , degeneracy $d (G)$ , and m…