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arXiv · 2401.00666

On the $δ$-chromatic numbers of the Cartesian products of graphs

Wipawee Tangjai·Witsarut Pho-on·Panupong Vichitkunakorn
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Abstract

In this work, we study the $δ$-chromatic number of a graph which is the chromatic number of the $δ$-complement of a graph. We give a structure of the $δ$-complements and sharp bounds on the $δ$-chromatic numbers of the Cartesian products of graphs. Furthermore, we compute the $δ$-chromatic numbers of various classes of Cartesian product graphs, including the Cartesian products between cycles, paths, and stars.

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Wipawee Tangjai, Witsarut Pho-on, Panupong Vichitkunakorn. 2024-01-01. On the $δ$-chromatic numbers of the Cartesian products of graphs. https://arxiv.org/abs/2401.00666

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