Graphs without even holes or diamonds

TL;DR

This paper proves that graphs lacking even holes and diamonds can be decomposed into simpler components with bounded cliquewidth, aiding in understanding their structure and algorithmic properties.

Contribution

It introduces a decomposition method for graphs without even holes and diamonds, showing they can be broken down into parts with bounded cliquewidth, a novel structural insight.

Findings

Graphs without even holes and diamonds can be decomposed via clique-separators.

Decomposed graphs have uniformly bounded cliquewidth.

This structural result facilitates algorithmic applications on such graphs.

Abstract

An even hole is an induced chordless cycle of even length at least four. A diamond is an induced subgraph isomorphic to K_4-e. We show that graphs without even holes and without diamonds can be decomposed via clique-separators into graphs that have uniformly bounded cliquewidth.