The Clique Complex and Hypergraph Matching

  title={The Clique Complex and Hypergraph Matching},
  author={R. Meshulam},
  • R. Meshulam
  • Published 2001
  • Mathematics, Computer Science
  • Combinatorica
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… Expand
A Tree Version of K ¨ Onig's Theorem
König's theorem states that the covering number and the matching number of a bipartite graph are equal. We prove a generalisation, in which the point in one fixed side of the graph of each edge isExpand
Independent systems of representatives in weighted graphs
A weighted generalization of a theorem of Haxell, on independent systems of representatives (ISR’s) is proved, which proves that there exists a coloring of the graph by 2Δ colors, where each color class meets each Vi at precisely one vertex. Expand
Matroid Representation of Clique Complexes
The quality of a greedy algorithm for the maximum weighted clique problem from the viewpoint of matroid theory is approached and the necessary and sufficient number of matroids for the representation of all graphs with n vertices is determined. Expand
Matroid representation of clique complexes
The quality of a greedy algorithm for the maximum weighted clique problem from the viewpoint of matroid theory is approached and the minimum number k such that the clique complex of a given graph can be represented as the intersection of k matroids is investigated. Expand
Domination numbers and noncover complexes of hypergraphs
An upper bound on their Leray numbers is obtained in terms of hypergraph domination numbers and the homotopy type of the noncover complexes of certain uniform hypergraphs, called tight paths and tight cycles are computed. Expand
Independent transversals and hypergraph matchings - an elementary approach
We give a self-contained elementary approach to a body of combinatorial results that were previously proved using topology. One example is the following hypergraph version of Hall’s Theorem, due toExpand
Degree Conditions for Matchability in 3-Partite Hypergraphs
A strong version of a theorem of Drisko (as generalized by the first two authors) is proved, that every family of matchings of size $2n-1$ in a bipartite graph has a partial rainbow matching of size n. Expand
Fractionally balanced hypergraphs and rainbow KKM theorems
A $d$-partite hypergraph is called fractionally balanced if there exists a non-negative function on its edge set that has constant degrees in each vertex side. Using a topological version of Hall'sExpand
A Note on Vertex List Colouring
  • P. Haxell
  • Mathematics, Computer Science
  • Combinatorics, Probability and Computing
  • 2001
It is proved that there exists a proper vertex colouring f of G such that f( v) ∈ S(v) for each v ∈ V(G) and this proves a weak version of a conjecture of Reed. Expand
A note on interconnecting matchings in graphs
We prove a sufficient condition for a graph G to have a matching that interconnects all the components of a disconnected spanning subgraph of G. The condition is derived from a recent extension ofExpand


Hall's theorem for hypergraphs
A hypergraph version of Hall's theorem is proved, which implies that A has a system of disjoint representatives if and only if jSBj jBj for every subfamily B A. Expand
Homology Theory: An Introduction to Algebraic Topology
This book is designed to be an introduction to some of the basic ideas in the field of algebraic topology. In particular, it is devoted to the foundations and applications of homology theory. TheExpand
Abstract : A determination is made of the homology groups of an important class of lattices called geometric lattices. (Author)
Topological methods
Topological methods, in: Handbook of Combinatorics
  • Eds.), 1819–1872,
  • 1995