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Perfectf-matchings andf-factors in hypergraphs—A combinatorial approach

2017
*
Discrete Mathematics
*

Keywords:

doi:10.1016/j.disc.2017.05.005
fatcat:5dff6egarbfqbmwwyd57h37i2i
*perfect*f -*matchings**in**hypergraphs*, f -factors*in**hypergraphs*, mengerian*hypergraph*,*balanced**hypergraph*,*perfect**hypergraph*, Hall's Theorem ... We prove characterizations of the existence of*perfect*f -*matchings**in*uniform mengerian and*perfect**hypergraphs*. Moreover, we investigate the f -factor problem*in**balanced**hypergraphs*. ... to the*perfect*f -*matching*problem*in**balanced**hypergraphs*we had f (v) ≤ 4 for all v ∈ V . ...##
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The Tight Cut Decomposition of Matching Covered Uniformable Hypergraphs
[article]

2019
*
arXiv
*
pre-print

The

arXiv:1812.05461v3
fatcat:li2ksb3xsfbehik44jbqjvcv2y
*perfect**matching*polytope, i.e. the convex hull of (incidence vectors of)*perfect**matchings*of a graph is used*in*many combinatorial algorithms. ... Moreover, we show how the tight cut decomposition leads to a decomposition of the*perfect**matching*polytope of uniformable*hypergraphs*and that the recognition problem for tight cuts*in*uniformable*hypergraphs*... We will add a new characterisation of*balanced**hypergraphs**in*terms of their*perfect**matching*polytope. ...##
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Computing the Partition Function for Perfect Matchings in a Hypergraph

2011
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Combinatorics, probability & computing
*

We also discuss applications to counting of

doi:10.1017/s0963548311000435
fatcat:kgg6u57hprbircrdmd5y4roz6u
*perfect*and nearly*perfect**matchings**in**hypergraphs*. ... When the weights w S are positive and within a constant factor, fixed*in*advance, of each other, we present a simple polynomial time algorithm to approximate the sum within a polynomial*in*m factor. ... Theorem 1.5 allows us to distinguish*in*polynomial time between*hypergraphs*that have sufficiently many*perfect**matchings*and*hypergraphs*that do not have nearly*perfect**matchings*. ...##
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Computing the partition function for perfect matchings in a hypergraph
[article]

2011
*
arXiv
*
pre-print

We also discuss applications to counting of

arXiv:1009.2397v3
fatcat:l54q6qgld5adpgwotodalvzrba
*perfect*and nearly*perfect**matchings**in**hypergraphs*. ... When the weights w_S are positive and within a constant factor, fixed*in*advance, of each other, we present a simple polynomial time algorithm to approximate the sum within a polynomial*in*m factor. ... Theorem 1.6 allows us to distinguish*in*polynomial time between*hypergraphs*that have sufficiently many*perfect**matchings*and*hypergraphs*that do not have nearly*perfect**matchings*. ...##
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Matchings in 3-uniform hypergraphs

2013
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Journal of combinatorial theory. Series B (Print)
*

Fact Let B be a

doi:10.1016/j.jctb.2012.11.005
fatcat:em4lylugxjbcnmxjyhkc3zroxu
*balanced*bipartite graph on 6 vertices. Then either B contains a*perfect**matching*; B ∼ = B 023 , B 033 , B 113 or; e(B) ≤ 4. ... Fact Let B be a*balanced*bipartite graph on 6 vertices. Then either B contains a*perfect**matching*; B ∼ = B 023 , B 033 , B 113 or; e(B) ≤ 4. ...##
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Perfect matchings in r-partite r-graphs

2009
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European journal of combinatorics (Print)
*

We prove that under this condition H must have a

doi:10.1016/j.ejc.2008.02.011
fatcat:wheqdrillbdybjoizyyq2qtbcq
*perfect**matching*. This answers a question of Kuhn and Osthus. ... Suppose that there exist two sides of H, each satisfying the following condition: the degree of each legal (r-1)-tuple contained*in*the complement of this side is strictly larger than n/2. ... Suppose, furthermore, that the degree of every pair*in*(V 1 × V 2 ) is 1 and the degree of every pair*in*(V 1 × V 3 ) is at most 1 . Then there exists*in*H a*matching*of size n. ...##
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The Multilinear Polytope for Acyclic Hypergraphs

2018
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SIAM Journal on Optimization
*

Utilizing an equivalent

doi:10.1137/16m1095998
fatcat:6roknqn6jne3zlxw4yhddzltvy
*hypergraph*representation, we study the facial structure of the Multilinear polytope*in*conjunction with the acyclicity degree of the underlying*hypergraph*. ... As the Multilinear polytope for γ-acyclic*hypergraphs*may contain exponentially many facets*in*general, we present a highly efficient polynomial algorithm to solve the separation problem. ... [14] proved that a minimum-weight*perfect**matching**in**balanced**hypergraphs*can be obtained*in*polynomial time via solving a linear optimization problem. ...##
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Matchings in 3-uniform hypergraphs of large minimum vertex degree

2011
*
Electronic Notes in Discrete Mathematics
*

We determine the minimum vertex degree that ensures a

doi:10.1016/j.endm.2011.10.036
fatcat:ckcmpb562vbmhjle4o6tx3vedu
*perfect**matching**in*a 3uniform*hypergraph*. ... If the minimum vertex degree of H is greater than n−1 2 − 2n/3 2 , then H contains a*perfect**matching*. This bound is tight and answers a question of Hàn, Person and Schacht. ... Fact 2. 1 Fig. 1 . 11 Let B be a*balanced*bipartite graph on 6 vertices. • If e(B) ≥ 7 then B contains a*perfect**matching*. • If e(B) = 6 then either B contains a*perfect**matching*or B ∼ = B 033 . • If ...##
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Page 5399 of Mathematical Reviews Vol. , Issue 89J
[page]

1989
*
Mathematical Reviews
*

Let f(G) and g(G) be the number of

*perfect**matchings*of a factorable graph G and the number of maximum*matchings*of a nonfactorable graph G, respectively. ... Larry Basen§Spiler (Mobile, AL) 89j:05058 05C70 Zheng, Mao Lin (PRC-BJ) On the*perfect**matchings*and the maximum*matchings*of n-connected graphs. (Chinese. English summary) Comm. Appl. Math. ...##
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Matchings and Hamilton cycles in hypergraphs

2005
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Discrete Mathematics & Theoretical Computer Science
*

International audience It is well known that every bipartite graph with vertex classes of size $n$ whose minimum degree is at least $n/2$ contains a

doi:10.46298/dmtcs.3457
fatcat:bkevf5myg5b3vmf7e63fg4qquu
*perfect**matching*. ... that every pair of consecutive vertices lies*in*a hyperedge which consists of three consecutive vertices. ...*Matchings**in*uniform*hypergraphs*The so called 'marriage theorem' of Hall provides a necessary and sufficient condition for the existence of a*perfect**matching**in*a bipartite graph. ...##
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Node-balancing by edge-increments
[article]

2015
*
arXiv
*
pre-print

*In*this paper we study several variants of this problem for graphs and

*hypergraphs*. ... On the combinatorial side we show connections with fundamental results from

*matching*theory such as Hall's Theorem and Tutte's Theorem. ... This follows by a reduction from 3-dimensional

*matching*[11] . Thus deciding whether a

*hypergraph*has a

*perfect*

*matching*is an NPcomplete problem. ...

##
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Node-Balancing by Edge-Increments
[chapter]

2015
*
Lecture Notes in Computer Science
*

*In*this paper we study several variants of this problem for graphs and

*hypergraphs*. ... On the combinatorial side we show connections with fundamental results from

*matching*theory such as Hall's Theorem and Tutte's Theorem. ... This follows by a reduction from 3-dimensional

*matching*[11] . Thus deciding whether a

*hypergraph*has a

*perfect*

*matching*is an NPcomplete problem. ...

##
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An Approximation Result for Matchings in Partitioned Hypergraphs
[chapter]

2016
*
Operations Research Proceedings
*

We investigate the

doi:10.1007/978-3-319-28697-6_5
dblp:conf/or/BeckenbachB14
fatcat:vnroapptfjgm7g6qu4vhoouf4i
*matching*and*perfect**matching*polytopes of*hypergraphs*having a special structure, which we call partitioned*hypergraphs*. ... We show that the integrality gap of the standard LP-relaxation is at most 2 √ d for partitioned*hypergraphs*with parts of size ≤ d. ... The*hypergraph*assignment problem can also be seen as a*perfect**matching*problem*in*a*hypergraph*having the following special structure: Definition. ...##
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Perfect fractional matchings in k-out hypergraphs
[article]

2017
*
arXiv
*
pre-print

*In*particular, we show that for each r there is a k=k(r) such that the k-out r-uniform

*hypergraph*on n vertices has a

*perfect*fractional

*matching*with high probability (i.e., with probability tending to ... This is based on a new notion of

*hypergraph*expansion and the observation that sufficiently expansive

*hypergraphs*admit

*perfect*fractional

*matchings*. ... A

*perfect*

*matching*

*in*a

*hypergraph*is a collection of edges partitioning the vertex set. ...

##
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Dynamic load-balancing with variable number of processors based on graph repartitioning

2012
*
2012 19th International Conference on High Performance Computing
*

*In*this paper, we present a new graph repartitioning algorithm which accepts to dynamically change the number of processors, assuming the load is already

*balanced*. ... These approaches can be very inefficient, especially

*in*terms of resource consumption. ...

*In*this paper, we focus on

*perfect*communication matrix, which results from two perfectly

*balanced*partitions, P and P . ...

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