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Nearly complete graphs decomposable into large induced matchings and their applications

Noga AlonAnkur MoitraBenjamin Sudakov — 2013

Journal of the European Mathematical Society

We describe two constructions of (very) dense graphs which are edge disjoint unions of large induced matchings. The first construction exhibits graphs on N vertices with ( N 2 ) - o ( N 2 ) edges, which can be decomposed into pairwise disjoint induced matchings, each of size N 1 - o ( 1 ) . The second construction provides a covering of all edges of the complete graph K N by two graphs, each being the edge disjoint union of at most N 2 - δ induced matchings, where δ > 0 , 076 . This disproves (in a strong form) a conjecture of Meshulam, substantially...

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