All Subgraphs of a Wheel are 5-Coupled-Choosable

TL;DR

This paper proves that all subgraphs of wheel graphs are 5-coupled-choosable, providing a linear-time coloring algorithm and establishing the tightness of the bound for wheel graphs with at least five vertices.

Contribution

It establishes the 5-coupled-choosability of all subgraphs of wheel graphs and presents a linear-time coloring method, also demonstrating the bound's tightness.

Findings

All subgraphs of wheel graphs are 5-coupled-choosable.

A linear-time algorithm exists for this coloring.

The bound of 5 is tight for wheel graphs with at least 5 vertices.

Abstract

A wheel graph consists of a cycle along with a center vertex connected to every vertex in the cycle. In this paper we show that every subgraph of a wheel graph has list coupled chromatic number at most 5, and this coloring can be found in linear time. We further show that `5' is tight for every wheel graph with at least 5 vertices, and briefly discuss possible generalizations to planar graphs of treewidth 3.