Classes of graphs without star forests and related graphs

Aistis Atminas

doi:10.1016/j.disc.2022.113089

Classes of graphs without star forests and related graphs

Aistis Atminas

Department of Pure Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

This work provides a structural characterisation of hereditary graph classes that do not contain a star forest, several graphs obtained from star forests by subset complementation, a union of cliques, and the complement of a union of cliques as induced subgraphs. This provides, for instance, structural results for graph classes not containing a matching and several complements of a matching. In terms of the speed of hereditary graph classes, our results imply that all such classes have at most factorial speed of growth.

Original language	English
Article number	113089
Journal	Discrete Mathematics
Volume	345
Issue number	12
DOIs	https://doi.org/10.1016/j.disc.2022.113089
Publication status	Published - Dec 2022

Keywords

Factorial speed of growth
Matchings
Monotone grid classes for permutations
Star forests

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10.1016/j.disc.2022.113089

Cite this

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abstract = "This work provides a structural characterisation of hereditary graph classes that do not contain a star forest, several graphs obtained from star forests by subset complementation, a union of cliques, and the complement of a union of cliques as induced subgraphs. This provides, for instance, structural results for graph classes not containing a matching and several complements of a matching. In terms of the speed of hereditary graph classes, our results imply that all such classes have at most factorial speed of growth.",

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AB - This work provides a structural characterisation of hereditary graph classes that do not contain a star forest, several graphs obtained from star forests by subset complementation, a union of cliques, and the complement of a union of cliques as induced subgraphs. This provides, for instance, structural results for graph classes not containing a matching and several complements of a matching. In terms of the speed of hereditary graph classes, our results imply that all such classes have at most factorial speed of growth.

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KW - Matchings

KW - Monotone grid classes for permutations

KW - Star forests

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Classes of graphs without star forests and related graphs

Abstract

Keywords

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