The chromatic number of heptagraphs

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-03-19 DOI:10.1002/jgt.23094

Di Wu, Baogang Xu, Yian Xu

引用次数: 0

Abstract

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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七段体的色度数

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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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .