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On the Inapproximability of Vertex Cover on kPartite kUniform Hypergraphs
"... Computing a minimum vertex cover in graphs and hypergraphs is a wellstudied optimizaton problem. While intractable in general, it is well known that on bipartite graphs, vertex cover is polynomial time solvable. In this work, we study the natural extension of bipartite vertex cover to hypergraphs, ..."
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, namely finding a small vertex cover in kuniform kpartite hypergraphs, when the kpartition is given as input. For this problem Lovász [16] gave a k 2 factor LP rounding based approximation, and a matching ( k 2 − o(1)) integrality gap instance was constructed by Aharoni et al. [1]. We prove
Rainbow Matchings and Hamilton Cycles in Random Graphs
, 2014
"... Let HPn,m,k be drawn uniformly from all kuniform, kpartite hypergraphs where each part of the partition is a disjoint copy of [n]. We let HP (κ) n,m,k be an edge colored version, where we color each edge randomly from one of κ colors. We show that if κ = n and m = Kn log n where K is sufficiently ..."
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Let HPn,m,k be drawn uniformly from all kuniform, kpartite hypergraphs where each part of the partition is a disjoint copy of [n]. We let HP (κ) n,m,k be an edge colored version, where we color each edge randomly from one of κ colors. We show that if κ = n and m = Kn log n where K is sufficiently
Rainbow Hamilton cycles in uniform hypergraphs
"... be the complete kuniform hypergraph, k ≥ 3, and let ℓ be an integer such that 1 ≤ ℓ ≤ k − 1 and k − ℓ divides n. An ℓoverlapping Hamilton cycle in K (k) n is a spanning subhypergraph C of K (k) n with n/(k − ℓ) edges and such that for some cyclic ordering of the vertices each edge of C consists of ..."
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be the complete kuniform hypergraph, k ≥ 3, and let ℓ be an integer such that 1 ≤ ℓ ≤ k − 1 and k − ℓ divides n. An ℓoverlapping Hamilton cycle in K (k) n is a spanning subhypergraph C of K (k) n with n/(k − ℓ) edges and such that for some cyclic ordering of the vertices each edge of C consists
Independence and Matchings in σhypergraphs
"... Let σ be a partition of the positive integer r. A σhypergraph H = H(n, r, qσ) is an runiform hypergraph on nq vertices which are partitioned into n classes V1, V2,..., Vn each containing q vertices. An rsubset K of vertices is an edge of the hypergraph if the partition of r formed by the nonze ..."
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Let σ be a partition of the positive integer r. A σhypergraph H = H(n, r, qσ) is an runiform hypergraph on nq vertices which are partitioned into n classes V1, V2,..., Vn each containing q vertices. An rsubset K of vertices is an edge of the hypergraph if the partition of r formed by the non
Coverings and Matchings in rPartite Hypergraphs
, 2010
"... Ryser’s conjecture postulates that, for rpartite hypergraphs, τ ≤ (r − 1)ν where τ is the covering number of the hypergraph and ν is the matching number. Although this conjecture has been open since the 1960’s, researchers have resolved it for special cases such as for intersecting hypergraphs wher ..."
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Ryser’s conjecture postulates that, for rpartite hypergraphs, τ ≤ (r − 1)ν where τ is the covering number of the hypergraph and ν is the matching number. Although this conjecture has been open since the 1960’s, researchers have resolved it for special cases such as for intersecting hypergraphs
Rainbow matchings in rpartite rgraphs
"... Given a collection of matchings M = (M1,M2,...,Mq) (repetitions allowed), a matching M contained in ⋃ M is said to be srainbow for M if it contains representatives from s matchings Mi (where each edge is allowed to represent just one Mi). Formally, this means that there is a function φ: M → [q] suc ..."
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] such that e ∈ M φ(e) for all e ∈ M, and Im(φ)  � s. Let f(r,s,t) be the maximal k for which there exists a set of k matchings of size t in some rpartite hypergraph, such that there is no srainbow matching of size t. We prove that f(r,s,t) � 2 r−1 (s − 1), make the conjecture that equality holds for all
On Linear and Semidefinite Programming Relaxations for Hypergraph Matching
"... The hypergraph matching problem is to find a largest collection of disjoint hyperedges in a hypergraph. This is a wellstudied problem in combinatorial optimization and graph theory with various applications. The best known approximation algorithms for this problem are all local search algorithms. I ..."
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proof of a result of Füredi, Kahn and Seymour, showing that the integrality gap is exactly k − 1 + 1/k for kuniform hypergraphs, and is exactly k − 1 for kpartite hypergraphs. This yields an improved approximation algorithm for the weighted 3dimensional matching problem. Our algorithm combines
COMPUTING THE PARTITION FUNCTION FOR PERFECT MATCHINGS IN A Hypergraph
, 2011
"... Given nonnegative weights wS on the ksubsets S of a kmelement set V, we consider the sum of the products wS1 · · · wSm over all partitions V = S1 ∪... ∪ Sm into pairwise disjoint ksubsets Si. When the weights wS are positive and within a constant factor, fixed in advance, of each other, we pre ..."
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Cited by 13 (5 self)
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Given nonnegative weights wS on the ksubsets S of a kmelement set V, we consider the sum of the products wS1 · · · wSm over all partitions V = S1 ∪... ∪ Sm into pairwise disjoint ksubsets Si. When the weights wS are positive and within a constant factor, fixed in advance, of each other, we
Rainbow Hfactors of complete suniform rpartite hypergraphs
, 2008
"... We say a suniform rpartite hypergraph is complete, if it has a vertex partition {V1, V2,..., Vr} of r classes and its hyperedge set consists of all the ssubsets of its vertex set which have at most one vertex in each vertex class. We denote the complete suniform rpartite hypergraph with k verti ..."
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We say a suniform rpartite hypergraph is complete, if it has a vertex partition {V1, V2,..., Vr} of r classes and its hyperedge set consists of all the ssubsets of its vertex set which have at most one vertex in each vertex class. We denote the complete suniform rpartite hypergraph with k
How many colors guarantee a rainbow matching?
, 2009
"... Abstract Given a coloring of the edges of a multihypergraph, a rainbow tmatching is a collection of t disjoint edges, each having a different color. In this note we study the problem of finding a rainbow tmatching in an rpartite runiform multihypergraph whose edges are colored with f colors s ..."
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Abstract Given a coloring of the edges of a multihypergraph, a rainbow tmatching is a collection of t disjoint edges, each having a different color. In this note we study the problem of finding a rainbow tmatching in an rpartite runiform multihypergraph whose edges are colored with f colors
Results 1  10
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22