Degree choosable signed graphs
Thomas Schweser, Michael Stiebitz

TL;DR
This paper extends Brooks' theorem to signed graphs with multiple edges, characterizes degree choosable signed graphs, and explores properties of color critical signed graphs.
Contribution
It generalizes Brooks' theorem for signed graphs with multiple edges and provides a characterization of degree choosable signed graphs.
Findings
Extended Brooks' type result to graphs with multiple edges.
Characterized degree choosable signed graphs.
Established basic properties of color critical signed graphs.
Abstract
A signed graph is a graph in which each edge is labeled with or . A (proper) vertex coloring of a signed graph is a mapping that assigns to each vertex a color such that every edge of satisfies , where is the sign of the edge . For an integer , let and . Following \cite{MaRS2015}, the signed chromatic number of is the least integer such that admits a vertex coloring with . As proved in \cite{MaRS2015}, every signed graph satisfies and there are three types of signed connected simple graphs for which equality holds. We will extend this Brooks' type result by considering graphs having multiple edges. We will also proof a list version of…
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