## Horizons of CombinatoricsErvin Gyori, Gyula O.H. Katona, László Lovász Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, combinatorial geometry as well. The recent volume contains high level surveys on these topics with authors mostly being invited speakers for the conference "Horizons of Combinatorics" held in Balatonalmadi, Hungary in 2006. The collection gives a very good overview of recent trends and results in a large part of combinatorics and related topics, and offers an interesting reading for experienced specialists as well as to young researchers and students. |

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2-factor adjacency matrix Ahlswede algorithm assume ballot theorem bar-and-joint framework bipartite C-edges chromatic number chromatic spectrum clique combinatorics components condition conjecture connected consider construction contains convex sets cycle defined denote description complexity disjoint distribution edges elements Erdos estimate example exists finite graph G Graph Theory Hence holds hypercube implies independent set induced induced subgraph infinite graphs Infinite Theorem intersection graph La(n least Lemma Let G linear lower bound Mathematics matrix maximal maximum number obtained Pach pair partially ordered partition partition regular permutations plane polygonal graphs poset positive constant probability problem proved question Ramsey Ramsey theory random graph random matrix random variables random walk real numbers rigid semialgebraic sets spanR stochastic processes subgraph subposet subsums tensegrity tensegrity framework Theorem 5.1 trivial Tuza uncolorable uniquely colorable upper bound upper chromatic vectors vertex set Voloshin x-monotone curves zero