Self-colorings of graphs

Department

Mathematics

Document Type

Article

Publication Date

1-1-2023

Abstract

Abstract. Suppose that G and H are finite simple graphs on the same vertex set V. We will say that H is G-colorable if H is properly colorable from the list assignment NG, i.e., the assignment of NG(v) as a list of colors to each v ϵ V. If G itself is G-colorable, we will say that G is self-colorable. It is shown that every graph G with no isolated vertices is self-colorable. A necessary and sufficient condition on G for its complement to be G-colorable is proven. Multicolorings from the NG list assignment are considered and questions are posed. We owe this inquiry to one of Steve Hedetniemi’s seminal questions [1].

Journal Title

Bulletin of the Institute of Combinatorics and its Applications

Journal ISSN

11831278

Volume

97

First Page

106

Last Page

116

Digital Object Identifier (DOI)

NA

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