Abstract
Given a graph G, its k-coloring graph has vertex set given by the proper k-colorings of the vertices of G with two k-colorings adjacent if and only if they differ at exactly one vertex. Beier et al. (Discrete Math. 339:8 (2016), 2100–2112) give various characterizations of coloring graphs, including finding graphs which never arise as induced subgraphs of coloring graphs. These are called forbidden subgraphs, and if no proper subgraph of a forbidden subgraph is forbidden, it is called minimal forbidden. In this paper, we construct a finite collection of minimal forbidden subgraphs that come from modifying theta graphs. We also construct an infinite family of minimal forbidden subgraphs similar to the infinite family found by Beier et al.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
