Forbidden induced subgraph characterization of circle graphs within split graphs
Discrete Mathematics
2023-04-04 v1 Combinatorics
Abstract
A graph is circle if its vertices are in correspondence with a family of chords in a circle in such a way that every two distinct vertices are adjacent if and only if the corresponding chords have nonempty intersection. Even though there are diverse characterizations of circle graphs, a structural characterization by minimal forbidden induced subgraphs for the entire class of circle graphs is not known, not even restricted to split graphs (which are the graphs whose vertex set can be partitioned into a clique and a stable set). In this work, we give a characterization by minimal forbidden induced subgraphs of circle graphs, restricted to split graphs.
Cite
@article{arxiv.2007.00570,
title = {Forbidden induced subgraph characterization of circle graphs within split graphs},
author = {Flavia Bonomo-Braberman and Guillermo A. Durán and Nina Pardal and Martín D. Safe},
journal= {arXiv preprint arXiv:2007.00570},
year = {2023}
}
Comments
59 pages, 15 figures