用三角形覆盖图形边缘

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-09-03 DOI:10.1016/j.disc.2024.114226

Csilla Bujtás , Akbar Davoodi , Laihao Ding , Ervin Győri , Zsolt Tuza , Donglei Yang

引用次数: 0

摘要

在图 G 中，让 ρ△(G) 表示覆盖 G 所有边的边集和三角形的最小大小，让 α1(G) 表示每个三角形中最多包含一条边的边集的最大大小。受 Erdős、Gallai 和 Tuza 问题的启发，我们研究了 ρ△(G) 和 α1(G) 之间的关系，并建立了 ρ△(G) 的尖锐上界。我们还证明了所考虑的不变式的 Nordhaus-Gaddum 型不等式。

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Covering the edges of a graph with triangles

In a graph G, let $ρ_{△} (G)$ denote the minimum size of a set of edges and triangles that cover all edges of G, and let $α_{1} (G)$ be the maximum size of an edge set that contains at most one edge from each triangle. Motivated by a question of Erdős, Gallai, and Tuza, we study the relationship between $ρ_{△} (G)$ and $α_{1} (G)$ and establish a sharp upper bound on $ρ_{△} (G)$ . We also prove Nordhaus-Gaddum-type inequalities for the considered invariants.

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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.