On the zero-free region for the chromatic polynomial of graphs with maximum degree Δ and girth g

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-10-09 DOI:10.1016/j.disc.2025.114825

Paula M.S. Fialho , Emanuel Juliano , Aldo Procacci

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引用次数: 0

Abstract

The purpose of the present paper is to provide, for all pairs of integers

(Δ, g)

with

Δ \geq 3

and

g \geq 3

, a positive number

C (Δ, g)

such that chromatic polynomial

P_{G} (q)

of a graph

G

with maximum degree Δ and finite girth g is free of zero if

| q | \geq C (Δ, g)

. Our bounds enlarge the zero-free region in the complex plane of

P_{G} (q)

in comparison to all previous bounds. In particular, for small values of Δ our estimates yield an expressive improvement on the bounds recently obtained by Jenssen, Patel and Regts in [J. Comb. Theor. B, 169 (2024)], while they coincide with their estimates when

Δ \to \infty

查看原文本刊更多论文

周长为g的最大度Δ图的色多项式的无零区域

本文的目的是给出对于Δ≥3且g≥3的所有整数对（Δ，g），当|q|≥C（Δ，g）时，最大度为Δ且有限周长为g的图g的色多项式PG(q)不为零的正数C（Δ，g）。与以前的边界相比，我们的边界扩大了PG(q)复平面上的无零区域。特别是，对于Δ的小值，我们的估计在最近由Jenssen， Patel和Regts在[J]中得到的边界上产生了表达性的改进。合成杆。定理。B, 169(2024)]，而当Δ→∞时，它们与他们的估计一致。

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

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.