On wheel-free graphs
Pierre Aboulker, Fr\'ed\'eric Havet, Nicolas Trotignon
TL;DR
This paper investigates wheel-free graphs, proving that 3-connected wheel-free graphs are minimally 3-connected and providing a new proof that such graphs are 3-colorable, contributing to graph theory understanding.
Contribution
It offers a new proof of the 3-colorability of wheel-free graphs and characterizes 3-connected wheel-free graphs as minimally 3-connected.
Findings
3-connected wheel-free graphs are minimally 3-connected
Wheel-free graphs are 3-colorable
New proof of Thomassen and Toft's theorem
Abstract
A wheel is a graph formed by a chordless cycle and a vertex that has at least three neighbors in the cycle. We prove that every 3-connected graph that does not contain a wheel as a subgraph is in fact minimally 3-connected. We give a new proof of a theorem of Thomassen and Toft: every graph that does not contain a wheel as a subgraph is 3-colorable.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Graph Labeling and Dimension Problems