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Results 1 - 10
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22
On the Inapproximability of Vertex Cover on k-Partite k-Uniform Hypergraphs
"... Computing a minimum vertex cover in graphs and hypergraphs is a well-studied 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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Cited by 6 (0 self)
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, namely finding a small vertex cover in k-uniform k-partite hypergraphs, when the k-partition 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 k-uniform, k-partite 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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Cited by 1 (0 self)
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Let HPn,m,k be drawn uniformly from all k-uniform, k-partite 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 k-uniform hypergraph, k ≥ 3, and let ℓ be an integer such that 1 ≤ ℓ ≤ k − 1 and k − ℓ divides n. An ℓ-overlapping 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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Cited by 6 (1 self)
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be the complete k-uniform hypergraph, k ≥ 3, and let ℓ be an integer such that 1 ≤ ℓ ≤ k − 1 and k − ℓ divides n. An ℓ-overlapping 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 σ-hypergraphs
"... Let σ be a partition of the positive integer r. A σ-hypergraph H = H(n, r, q|σ) is an r-uniform hypergraph on nq vertices which are parti-tioned into n classes V1, V2,..., Vn each containing q vertices. An r-subset K of vertices is an edge of the hypergraph if the partition of r formed by the non-ze ..."
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Let σ be a partition of the positive integer r. A σ-hypergraph H = H(n, r, q|σ) is an r-uniform hypergraph on nq vertices which are parti-tioned into n classes V1, V2,..., Vn each containing q vertices. An r-subset K of vertices is an edge of the hypergraph if the partition of r formed by the non
Coverings and Matchings in r-Partite Hypergraphs
, 2010
"... Ryser’s conjecture postulates that, for r-partite 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 r-partite 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 r-partite r-graphs
"... Given a collection of matchings M = (M1,M2,...,Mq) (repetitions allowed), a matching M contained in ⋃ M is said to be s-rainbow 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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Cited by 2 (0 self)
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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 r-partite hypergraph, such that there is no s-rainbow 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 well-studied 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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Cited by 16 (0 self)
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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 k-uniform hypergraphs, and is exactly k − 1 for k-partite hypergraphs. This yields an improved approximation algorithm for the weighted 3-dimensional matching problem. Our algorithm combines
COMPUTING THE PARTITION FUNCTION FOR PERFECT MATCHINGS IN A Hypergraph
, 2011
"... Given non-negative weights wS on the k-subsets S of a km-element set V, we consider the sum of the products wS1 · · · wSm over all partitions V = S1 ∪... ∪ Sm into pairwise disjoint k-subsets 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 non-negative weights wS on the k-subsets S of a km-element set V, we consider the sum of the products wS1 · · · wSm over all partitions V = S1 ∪... ∪ Sm into pairwise disjoint k-subsets Si. When the weights wS are positive and within a constant factor, fixed in advance, of each other, we
Rainbow H-factors of complete s-uniform r-partite hypergraphs
, 2008
"... We say a s-uniform r-partite hypergraph is complete, if it has a vertex partition {V1, V2,..., Vr} of r classes and its hyperedge set consists of all the s-subsets of its vertex set which have at most one vertex in each vertex class. We denote the complete s-uniform r-partite hypergraph with k verti ..."
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We say a s-uniform r-partite hypergraph is complete, if it has a vertex partition {V1, V2,..., Vr} of r classes and its hyperedge set consists of all the s-subsets of its vertex set which have at most one vertex in each vertex class. We denote the complete s-uniform r-partite hypergraph with k
How many colors guarantee a rainbow matching?
, 2009
"... Abstract Given a coloring of the edges of a multi-hypergraph, a rainbow t-matching is a collection of t disjoint edges, each having a different color. In this note we study the problem of finding a rainbow t-matching in an r-partite r-uniform multi-hypergraph whose edges are colored with f colors s ..."
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Abstract Given a coloring of the edges of a multi-hypergraph, a rainbow t-matching is a collection of t disjoint edges, each having a different color. In this note we study the problem of finding a rainbow t-matching in an r-partite r-uniform multi-hypergraph whose edges are colored with f colors
Results 1 - 10
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22
