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arXiv · 2103.11092

An improved bound on the chromatic number of the Pancake graphs

Leen Droogendijk·Elena V. Konstantinova
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Abstract

In this paper an improved bound on the chromatic number of the Pancake graph $P_n, n\geqslant 2$, is presented. The bound is obtained using a subadditivity property of the chromatic number of the Pancake graph. We also investigate an equitable coloring of $P_n$. An equitable $(n-1)$-coloring based on efficient dominating sets is given and optimal equitable $4$-colorings are considered for small $n$. It is conjectured that the chromatic number of $P_n$ coincides with its equitable chromatic number for any $n\geqslant 2$.

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Leen Droogendijk, Elena V. Konstantinova. 2021-03-20. An improved bound on the chromatic number of the Pancake graphs. https://doi.org/10.7151/dmgt.2432

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