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arXiv · 1903.03311

Optimal proper connection of graphs

Shinya Fujita
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Abstract

An edge-colored graph $G$ is called properly colored if no two adjacent edges share a color in $G$. An edge-colored connected graph $G$ is called properly connected if between every pair of distinct vertices, there exists a path that is properly colored. In this paper, we discuss how to make a connected graph properly connected efficiently. More precisely, we consider the problem to convert a given monochromatic graph into properly connected by recoloring $p$ edges with $q$ colors so that $p+q$ is as small as possible. We discuss how this can be done efficiently for some restricted graphs, such as trees, complete bipartite graphs and graphs with independence number $2$.

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Shinya Fujita. 2019-03-08. Optimal proper connection of graphs. https://arxiv.org/abs/1903.03311

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