对于没有5‐孔的图形，请访问Erdős-Hajnal

IF 1.5 1区数学 Q1 MATHEMATICS

Proceedings of the London Mathematical Society Pub Date : 2023-01-31 DOI:10.1112/plms.12504

Maria Chudnovsky, Alex Scott, Paul Seymour, Sophie Spirkl

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引用次数: 5

摘要

Erdős-Hajnal猜想说，对于每一个图都存在这样的存在，即每一个不包含诱导子图的图至少有一个团或稳定的基数集。我们证明当一个循环的长度为5时，这是成立的。我们还进一步证明了几个结果:例如，如果是一个循环并且是一个森林的补，那么存在这样的存在，即每个图都不包含这两个图作为诱导子图，至少有一个团或稳定的基数集。

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Erdős–Hajnal for graphs with no 5‐hole

Abstract The Erdős–Hajnal conjecture says that for every graph there exists such that every graph not containing as an induced subgraph has a clique or stable set of cardinality at least . We prove that this is true when is a cycle of length five. We also prove several further results: for instance, that if is a cycle and is the complement of a forest, there exists such that every graph containing neither of as an induced subgraph has a clique or stable set of cardinality at least .

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来源期刊

Proceedings of the London Mathematical Society 数学-数学

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Proceedings of the London Mathematical Society is the flagship journal of the LMS. It publishes articles of the highest quality and significance across a broad range of mathematics. There are no page length restrictions for submitted papers. The Proceedings has its own Editorial Board separate from that of the Journal, Bulletin and Transactions of the LMS.