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arXiv · 2003.06803

On perfect colorings of infinite multipath graphs

M. A. Lisitsyna·S. V. Avgustinovich·O. G. Parshina
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Abstract

A coloring of vertices of a given graph is called perfect if the color structure of each ball of radius $1$ in the graph depends only on the color of the ball center. Let $n$ be a positive integer. We consider a lexicographic product of the infinite path graph and a graph $G$ that can be either the complete or empty graph on $n$ vertices. We give a complete description of perfect colorings with an arbitrary number of colors of such graph products.

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M. A. Lisitsyna, S. V. Avgustinovich, O. G. Parshina. 2021-08-01. On perfect colorings of infinite multipath graphs. https://doi.org/10.33048/semi.2020.17.139

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