七段体的色度数

Pub Date : 2024-03-19 DOI:10.1002/jgt.23094

Di Wu, Baogang Xu, Yian Xu

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引用次数: 0

摘要

五段图是没有长度为 3 或 4 的循环且没有奇数长度至少为 7 的诱导循环的图形，七段图是没有长度小于 7 的循环且没有奇数长度至少为 9 的诱导循环的图形。Chudnovsky 和 Seymour 证明了每个五段都是 3 色的。在本文中，我们将证明每个七段都是 3 色的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The chromatic number of heptagraphs

A pentagraph is a graph without cycles of length 3 or 4 and without induced cycles of odd length at least 7, and a heptagraph is one without cycles of length less than 7 and without induced cycles of odd length at least 9. Chudnovsky and Seymour proved that every pentagraph is 3-colorable. In this paper, we show that every heptagraph is 3-colorable.

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