A reduction of the “cycles plus K4's” problem

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-07-28 DOI:10.1016/j.disc.2025.114696

Aseem Dalal , Jessica McDonald , Songling Shan

引用次数: 0

Abstract

Let H be a 2-regular graph and let G be obtained from H by gluing in vertex-disjoint copies of

K_{4}

. The “cycles plus

K_{4}

's” problem is to show that G is 4-colourable; this is a special case of the Strong Colouring Conjecture. In this paper we reduce the “cycles plus

K_{4}

's” problem to a specific 3-colourability problem. In the 3-colourability problem, vertex-disjoint triangles are glued (in a limited way) onto a disjoint union of triangles and paths of length at most 12, and we ask for 3-colourability of the resulting graph.

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减少了“循环加K4”的问题

设H是一个2正则图，设G是由H通过粘接K4的顶点不相交的副本得到的。“循环加K4”的问题是为了证明G是四色的；这是强着色猜想的一个特例。在本文中，我们将“循环加K4”问题简化为一个特定的3-可色性问题。在3色性问题中，顶点不相交的三角形（以有限的方式）粘在不相交的三角形和长度最多为12的路径上，我们要求生成的图具有3色性。

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.