将χ-有界性与多项式χ-有界性重新统一

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2025-08-28 DOI:10.1016/j.jctb.2025.08.002

Maria Chudnovsky , Linda Cook , James Davies , Sang-il Oum

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引用次数: 0

摘要

如果存在一个函数F，使得F中图的所有诱导子图H的χ(H)≤F (ω(H))，则一类图F是χ-有界的。如果F可以选择为多项式，则我们说F是多项式χ-有界的。Esperet提出了一个猜想，即每一类有χ有界的图都是多项式有χ有界的。这个猜想已经被推翻了；已经证明有一类图是χ有界的，但不是多项式χ有界的。然而，受Esperet猜想的启发，我们引入了波利安娜图类。如果C∩F对于每一个有χ有界的图类F都是多项式χ有界的，那么C类图就是波利安娜。我们证明了几类图是盲目乐观的，并给出了一些非盲目乐观图的适当类别。

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Reuniting χ-boundedness with polynomial χ-boundedness

A class

F

of graphs is χ-bounded if there is a function f such that

χ (H) \leq f (ω (H))

for all induced subgraphs H of a graph in

F

. If f can be chosen to be a polynomial, we say that

F

is polynomially χ-bounded. Esperet proposed a conjecture that every χ-bounded class of graphs is polynomially χ-bounded. This conjecture has been disproved; it has been shown that there are classes of graphs that are χ-bounded but not polynomially χ-bounded. Nevertheless, inspired by Esperet's conjecture, we introduce Pollyanna classes of graphs. A class

C

of graphs is Pollyanna if

C \cap F

is polynomially χ-bounded for every χ-bounded class

F

of graphs. We prove that several classes of graphs are Pollyanna and also present some proper classes of graphs that are not Pollyanna.

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来源期刊

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.