22 research outputs found
A Combinatorial Proof of Kneser'sConjecture*
Kneser's conjecture, first proved by LovĂĄsz in 1978, states that the graph with all k-element subsets of {1, 2, . . . , n} as vertices and with edges connecting disjoint sets has chromatic number nâ2k+2. We derive this result from Tucker's combinatorial lemma on labeling the vertices of special triangulations of the octahedral ball. By specializing a proof of Tucker's lemma, we obtain self-contained purely combinatorial proof of Kneser's conjectur
A generalization of Gale's lemma
In this work, we present a generalization of Gale's lemma. Using this
generalization, we introduce two combinatorial sharp lower bounds for and , two famous topological
lower bounds for the chromatic number of a graph
Some Ramsey- and anti-Ramsey-type results in combinatorial number theory and geometry
A szerzĆ nem jĂĄrult hozzĂĄ nyilatkozatĂĄban a dolgozat nyilvĂĄnossĂĄgra hozĂĄsĂĄhoz
Homology of Hom Complexes
The h The hom complex Hom(G,K) is the order complex of the poset composed of the graph multihomomorphisms from G to K. We use homology to provide conditions under which the hom complex is not contractible and derive a lower bound on the rank of its homology groups.om complex Hom(G,K) is the order complex of the poset composed of the graph multihomomorphisms from G to K. We use homology to provide conditions under which the hom complex is not contractible and derive a lower bound on the rank of its homology groups