Daniel W. Cranston

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3 papers · 1 filter

math.CO2025

Equitably Coloring Planar and Outerplanar Graphs

Daniel W. Cranston, Reem Mahmoud

A proper $s$ -coloring of an $n$ -vertex graph is \emph{equitable} if every color class has size $⌊ n / s ⌋$ or $⌈ n / s ⌉$ . A necessary condition to have an equita…

math.CO2025

Reconfiguration of List Colourings

Stijn Cambie, Wouter Cames van Batenburg, Daniel W. Cranston +2

Given a proper (list) colouring of a graph $G$ , a recolouring step changes the colour at a single vertex to another colour (in its list) that is currently unused on its neighbours,…

math.CO2024

Planar Graphs with Homomorphisms to the 9-cycle

Daniel W. Cranston, Jiaao Li, Zhouningxin Wang +1

We study the problem of finding homomorphisms into odd cycles from planar graphs with high odd-girth. The Jaeger-Zhang conjecture states that every planar graph of odd-girth at lea…