Classes of graphs without star forests and related graphs

TL;DR

This paper characterizes hereditary graph classes excluding star forests and related structures, revealing their structural properties and showing they grow at most factorially in size.

Contribution

It provides a new structural characterization of hereditary graph classes avoiding star forests and related graphs, with implications for their growth rates.

Findings

Hereditary classes excluding star forests have at most factorial growth.

Structural descriptions for classes avoiding matchings and their complements.

Results apply to various graph classes defined by forbidden induced subgraphs.

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.