On 4-chromatic Schrijver graphs: their structure, non-3-colorability, and critical edges

Abstract

We investigate 4-chromatic Schrijver graphs from various points of view and color-critical edges in Schrijver graphs in general. In particular, we present the following results. Our proof of non-3-colorability of 4-chromatic Schrijver graphs is based on a complete description of their structure that we present as well. This was already also given (in somewhat different terms) by Braun and even earlier in an unpublished manuscript by Li.