Density Conditions for k Vertex-Disjoint Triangles in Tripartite Graphs

IF 1 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2026-10-12 Epub Date: 2026-06-19 DOI:10.1002/jgt.70079

Mingyang Guo, Klas Markström

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引用次数: 0

Abstract

Let $n, k$ be positive integers such that $n \geq k$ and $G$ be a tripartite graph with parts $A, B, C$ such that $∣ A ∣ = ∣ B ∣ = ∣ C ∣ = n$ . Denote the edge densities of $G [A, B], G [A, C]$ and $G [B, C]$ by $α, β$ and $γ$ , respectively. In this paper, we study edge density conditions for the existence of $k$ vertex-disjoint triangles in a tripartite graph. For $n \geq 5 k + 2$ we give an optimal condition in terms of densities $α, β, γ$ for the existence of $k$ vertex-disjoint triangles in $G$ . We also give an optimal condition in terms of densities $α, β, γ$ for the existence of a triangle-factor in $G$ .

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三部图中k顶点不相交三角形的密度条件

设n。k为正整数，使得n≥k， G是一个有a， B，C满足∣A∣=∣B∣∣C∣= n。表示G [A]的边密度，B, B [a]；B .正确， C] by α；分别为β和γ。本文研究了一个三部图中k个顶点不相交三角形存在的边密度条件。对于n≥5k + 2，我们给出了密度的最优条件α, β，在G中存在k个顶点不相交三角形。我们也给出了密度α， β，在G中存在一个三角形因子。

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .