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# Tripartite Version of the Corr\'adi-Hajnal Theorem

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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.

### Most cited references3

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### Some Theorems on Abstract Graphs

(1952)
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### Blow-up Lemma

(1997)
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### On the maximal number of independent circuits in a graph

(1963)
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### Author and article information

###### Journal
2016-05-21
###### Article
10.1016/S0012-365X(01)00373-9
1605.06647

05C35, 05C70
Discrete Math. 254 (2002), no. 1-3, 289--308
22 pages, 4 figures
math.CO

Combinatorics