Edge coloring of products of signed graphs

Edge coloring of products of signed graphs

In 2020, Behr defined the problem of edge coloring of signed graphs and showed that every signed graph $(G, \sigma)$ can be colored using exactly $\Delta(G)$ or $\Delta(G) + 1$ colors, where $\Delta(G)$ is the maximum degree in graph $G$. In this paper, we focus on products of signed graphs. We reca...

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Hauptverfasser: Janczewski, Robert, Turowski, Krzysztof, Wróblewski, Bartłomiej
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Computer Science - Data Structures and Algorithms
Computer Science - Discrete Mathematics
Mathematics - Combinatorics
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Turowski, Krzysztof
Wróblewski, Bartłomiej
description In 2020, Behr defined the problem of edge coloring of signed graphs and showed that every signed graph $(G, \sigma)$ can be colored using exactly $\Delta(G)$ or $\Delta(G) + 1$ colors, where $\Delta(G)$ is the maximum degree in graph $G$. In this paper, we focus on products of signed graphs. We recall the definitions of the Cartesian, tensor, strong, and corona products of signed graphs and prove results for them. In particular, we show that $(1)$ the Cartesian product of $\Delta$-edge-colorable signed graphs is $\Delta$-edge-colorable, $(2)$ the tensor product of a $\Delta$-edge-colorable signed graph and a signed tree requires only $\Delta$ colors and $(3)$ the corona product of almost any two signed graphs is $\Delta$-edge-colorable. We also prove some results related to the coloring of products of signed paths and cycles.
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Computer Science - Discrete Mathematics
Mathematics - Combinatorics
title Edge coloring of products of signed graphs
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