Tripartite Version of the Corr\'adi-Hajnal Theorem

Csaba Magyar; Ryan R. Martin

doi:10.1016/S0012-365X(01)00373-9

Tripartite Version of the Corr\'adi-Hajnal Theorem

Combinatorics 2016-05-24 v1

Authors: Csaba Magyar , Ryan R. Martin

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Abstract

Let $G$ be a tripartite graph with $N$ vertices in each vertex class. If each vertex is adjacent to at least $(2/3)N$ vertices in each of the other classes, then either $G$ contains a subgraph that consists of $N$ vertex-disjoint triangles or $G$ is a specific graph in which each vertex is adjacent to exactly $(2/3)N$ vertices in each of the other classes.

Keywords

tripartite graphs Corrádi-Hajnal theorem vertex-disjoint triangles extremal graph theory adjacency condition

Cite

@article{arxiv.1605.06647,
  title  = {Tripartite Version of the Corr\'adi-Hajnal Theorem},
  author = {Csaba Magyar and Ryan R. Martin},
  journal= {arXiv preprint arXiv:1605.06647},
  year   = {2016}
}

Comments

22 pages, 4 figures

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