Nearly complete graphs decomposable into large induced matchings and their applications

@article{Alon2012NearlyCG,
  title={Nearly complete graphs decomposable into large induced matchings and their applications},
  author={Noga Alon and Ankur Moitra and Benny Sudakov},
  journal={ArXiv},
  year={2012},
  volume={abs/1111.0253}
}
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 (N2)-o(N2) edges, which can be decomposed into pairwise disjoint induced matchings, each of size N1-o(1). The second construction provides a covering of all edges of the complete graph KN by two graphs, each being the edge disjoint union of at most N2-δ induced matchings, where δ>0.076. This disproves (in a strong form) a… CONTINUE READING
2
Twitter Mentions

Similar Papers

Topics from this paper.

References

Publications referenced by this paper.
SHOWING 1-10 OF 11 REFERENCES

Private communication

J. Brody
  • 2012
VIEW 10 EXCERPTS
HIGHLY INFLUENTIAL

A new proof of the graph removal

J. Fox
  • lemma. Ann. of Math. 174,
  • 2011
VIEW 8 EXCERPTS
HIGHLY INFLUENTIAL

Simple analysis of graph tests for linearity and PCP

  • Random Struct. Algorithms
  • 2003
VIEW 9 EXCERPTS
HIGHLY INFLUENTIAL

Colored packing of sets

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Regular Partitions of Graphs

VIEW 8 EXCERPTS
HIGHLY INFLUENTIAL

On directed Steiner trees

VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL