Sure monochromatic subset sums
Nearly complete graphs decomposable into large induced matchings and their applications
We describe two constructions of (very) dense graphs which are edge disjoint unions of large induced matchings. The first construction exhibits graphs on vertices with edges, which can be decomposed into pairwise disjoint induced matchings, each of size . The second construction provides a covering of all edges of the complete graph by two graphs, each being the edge disjoint union of at most induced matchings, where . This disproves (in a strong form) a conjecture of Meshulam, substantially...
Explicit Ramsey graphs and orthonormal labelings.
Short certificates for tournaments.
-free graphs of large minimum degree.
On a generalization of Meyniel's conjecture on the Cops and Robbers game.
The maximum number of perfect matchings in graphs with a given degree sequence.
Perfect matchings in -regular graphs.
The number of -matchings in almost every tree is a zero residue.
Discrepancy games.
Another abstraction of the Erdős-Szekeres happy end theorem.
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