Combinatorics and Probability
Cambridge University Press, Mar 8, 2007 - Mathematics - 633 pages
Combinatorics is an area of mathematics involving an impressive breadth of ideas, and it encompasses topics ranging from codes and circuit design to algorithmic complexity and algebraic graph theory. In a highly distinguished career Béla Bollobás has made, and continues to make, many significant contributions to combinatorics, and this volume reflects the wide range of topics on which his work has had a major influence. It arises from a conference organized to mark his 60th birthday and the thirty-one articles contained here are of the highest calibre. That so many excellent mathematicians have contributed is testament to the very high regard in which Béla Bollobás is held. Students and researchers across combinatorics and related fields will find that this volume provides a wealth of insight to the state of the art.
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3-uniform hypergraph algorithm argument assume asymptotic Aut(r Aut(T bipartite graph Bollob´as branching process Cayley graph chromatic polynomial circuit circulant graph colouring Combinatorics complete bipartite graph complete block system complete graph computation conjecture consider constant contains Corollary cycle deﬁned deﬁnition degree denote diﬀerent disjoint distribution dual eigenvalues equivalent Erd˝os exists ﬁnd ﬁnite ﬁrst ﬁxed follows function giant component given graph G graphs of order Hamiltonian cycle Hence hyperedges hypergraph implies independent transversal induced induced subgraph inequality inﬁnite integer isomorphic least Let G linear lower bound Math maximum neighbours Note number of edges obtain order pq pair partition permutation probability problem proof of Theorem prove quasirandom random graph regularity lemma result satisﬁes satisfying Second Player Section sequence subgraph subsets suﬃciently Suppose symmetric Theorem Theorem 1.1 Theory upper bound vertex sets vertex-transitive graph vertices weak win winning sets