Involve: A Journal of Mathematics

• Involve
• Volume 11, Number 2 (2018), 311-324.

Forbidden subgraphs of coloring graphs

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.

Article information

Source
Involve, Volume 11, Number 2 (2018), 311-324.

Dates
Revised: 14 May 2017
Accepted: 19 June 2017
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.involve/1513775065

Digital Object Identifier
doi:10.2140/involve.2018.11.311

Mathematical Reviews number (MathSciNet)
MR3733960

Zentralblatt MATH identifier
06817023

Subjects
Primary: 05C15: Coloring of graphs and hypergraphs

Citation

Alvarado, Francisco; Butts, Ashley; Farquhar, Lauren; Russell, Heather M. Forbidden subgraphs of coloring graphs. Involve 11 (2018), no. 2, 311--324. doi:10.2140/involve.2018.11.311. https://projecteuclid.org/euclid.involve/1513775065

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