Transversals in a collection of stars or generic trees

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-10-10 DOI:10.1016/j.disc.2025.114836

Ethan Y.H. Li , Luyi Li , Ping Li

引用次数: 0

Abstract

Let

F

be a fixed collection of graphs on vertex set V and let

G

be a collection of elements in

F

. We investigate the transversal problem of finding the maximum value of

| G |

when

G

contains no rainbow element in

F

. In this paper, we determine the exact values and characterize all the extremal cases of

G

when

F

is a collection of stars or generic trees with the same order, respectively.

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星形集合或一般树的截线

设F是顶点集V上的一个固定图集合，设G是F中的一个元素集合，研究了当G在F中不含彩虹元素时求|G|最大值的截线问题。本文分别确定了F为同阶星形集合或一般树集合时G的所有极值情况，并给出了它们的精确值。

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.