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2017•White Rose Research Online (University of Leeds, The University of Sheffield, University of York)Requires access

On triangle-free graphs that do not contain a subdivision of the complete graph on four vertices as an induced subgraph

Trotignon, N, Vuskovic, K

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Abstract

We prove a decomposition theorem for the class of triangle-free graphs that do not contain a subdivision of the complete graph on four vertices as an induced subgraph. We prove that every graph of girth at least five in this class is 3-colorable.

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What this paper is about

We prove a decomposition theorem for the class of triangle-free graphs that do not contain a subdivision of the complete graph on four vertices as an induced subgraph. We prove that every graph of girth at least five in this class is 3-colorable.

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Available abstract

We prove a decomposition theorem for the class of triangle-free graphs that do not contain a subdivision of the complete graph on four vertices as an induced subgraph. We prove that every graph of girth at least five in this class is 3-colorable.

Key concepts: Combinatorics, Mathematics, Subdivision, Induced subgraph, Distance-hereditary graph, Discrete mathematics, Cograph, Graph homomorphism

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