10.9k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
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7 papers · 2 filters
Lower bounds for weak epsilon-nets and stair-convexity
Boris Bukh, Jiří Matoušek, Gabriel Nivasch
A set N is called a "weak epsilon-net" (with respect to convex sets) for a finite set X in R^d if N intersects every convex set that contains at least epsilon*|X| points of X. For…
Coloring plane graphs with independent crossings
Daniel Král', Ladislav Stacho
We show that every plane graph with maximum face size four whose all faces of size four are vertex-disjoint is cyclically 5-colorable. This answers a question of Albertson whether…
Geometric representation of binary codes and computation of weight enumerators
Pavel Rytíř
For every linear binary code , we construct a geometric triangular configuration so that the weight enumerator of is obtained by a simple formula from the weight enumera…
A combinatorial proof of the Removal Lemma for Groups
Daniel Král', Oriol Serra, Lluís Vena
Green [Geometric and Functional Analysis 15 (2005), 340--376] established a version of the Szemerédi Regularity Lemma for abelian groups and derived the Removal Lemma for abelian g…
Stabbing simplices by points and flats
Boris Bukh, Jiří Matoušek, Gabriel Nivasch
The following result was proved by Barany in 1982: For every d >= 1 there exists c_d > 0 such that for every n-point set S in R^d there is a point p in R^d contained in at least c_…
Long cycles in fullerene graphs
D. Král', O. Pangrác, J. -S. Sereni +1
It is conjectured that every fullerene graph is hamiltonian. Jendrol' and Owens proved [J. Math. Chem. 18 (1995), pp. 83--90] that every fullerene graph on n vertices has a cycle o…
Fullerene graphs have exponentially many perfect matchings
Frantisek Kardos, Daniel Král', Jozef Miskuf +1
A fullerene graph is a planar cubic 3-connected graph with only pentagonal and hexagonal faces. We show that fullerene graphs have exponentially many perfect matchings.