Roy Meshulam

On subsets of finite Abelian groups with no 3-term arithmetic progressions

Abstract Let G be a finite abelian group of odd order and let D(G) denote the maximal cardinality of a subset A ⊂ G which does not contain a 3-term arithmetic progression. It is shown that D(Zk1 ⊕ ⋯ ⊕ Zkn) ⩽ 2((k1 ⋯ kn/n). Together with results of Szemeredi and Heath-Brown it implies that there exists a β > 0 such that D(G) = O(∥G∥/(log ∥G∥)β) for all G.

Domination numbers and homology

Let I(G) denote the independence complex of a graph G = (V, E). Some relations between domination numbers of G and the homology of I(G) are given. As a consequence the following Hall-type conjecture of Aharoni is proved: Let γs*(G) denote the fractional star-domination number of G and let V =∪i=1m Vi be a partition of V into m classes.If γs*(G[∪i∈I Vi]) > |I| - 1 for all I ⊂ {1,...,m} then G contains an independent set which intersects all m classes.

THE CLIQUE COMPLEX AND HYPERGRAPH MATCHING

The width of a hypergraph is the minimal for which there exist such that for any , for some . The matching width of is the minimal such that for any matching there exist such that for any , for some . The following extension of the Aharoni-Haxell matching Theorem [3] is proved: Let be a family of hypergraphs such that for each either or , then there exists a matching such that for all . This is a consequence of a more general result on colored cliques in graphs. The proofs are topological and use the Nerve Theorem.

Collapsibility and Vanishing of Top Homology in Random Simplicial Complexes

Let

Intersections of Leray complexes and regularity of monomial ideals

\Delta _{n-1}

Expanders In Group Algebras

denote the

On the uniform-traffic capacity of single-hop interconnections employing shared directional multichannels

(n-1)