scholarly journals Space complexity of perfect matching in bounded genus bipartite graphs

2012 ◽  
Vol 78 (3) ◽  
pp. 765-779 ◽  
Author(s):  
Samir Datta ◽  
Raghav Kulkarni ◽  
Raghunath Tewari ◽  
N.V. Vinodchandran
Keyword(s):  
Perfect Matching ◽  
Bipartite Graphs ◽  
Space Complexity

Rainbow Perfect Matchings in Complete Bipartite Graphs: Existence and Counting

2013 ◽  
Vol 22 (5) ◽  
pp. 783-799 ◽  
Author(s):  
GUILLEM PERARNAU ◽  
ORIOL SERRA
Keyword(s):  
Bipartite Graph ◽  
High Probability ◽  
Perfect Matching ◽  
Complete Bipartite Graph ◽  
Bipartite Graphs ◽  
Perfect Matchings ◽  
Asymptotic Enumeration ◽  
Complete Bipartite Graphs ◽  
Edge Colourings ◽  
Square Matrix

A perfect matchingMin an edge-coloured complete bipartite graphKn,nis rainbow if no pair of edges inMhave the same colour. We obtain asymptotic enumeration results for the number of rainbow perfect matchings in terms of the maximum number of occurrences of each colour. We also consider two natural models of random edge-colourings ofKn,nand show that if the number of colours is at leastn, then there is with high probability a rainbow perfect matching. This in particular shows that almost every square matrix of ordernin which every entry appearsntimes has a Latin transversal.

scholarly journals Disimplicial arcs, transitive vertices, and disimplicial eliminations

2015 ◽  
Vol Vol. 17 no.2 (Graph Theory) ◽  
Author(s):  
Martiniano Eguia ◽  
Francisco Soulignac
Keyword(s):  
Efficient Algorithm ◽  
Bipartite Graphs ◽  
Space Complexity ◽  
Time And Space ◽  
Graph Classes ◽  
International Audience ◽  
Time And Space Complexity ◽  
Finite Posets

International audience In this article we deal with the problems of finding the disimplicial arcs of a digraph and recognizing some interesting graph classes defined by their existence. A <i>diclique</i> of a digraph is a pair $V$ &rarr; $W$ of sets of vertices such that $v$ &rarr; $w$ is an arc for every $v$ &isin; $V$ and $w$ &isin; $W$. An arc $v$ &rarr; $w$ is <i>disimplicial</i> when it belongs to a unique maximal diclique. We show that the problem of finding the disimplicial arcs is equivalent, in terms of time and space complexity, to that of locating the transitive vertices. As a result, an efficient algorithm to find the bisimplicial edges of bipartite graphs is obtained. Then, we develop simple algorithms to build disimplicial elimination schemes, which can be used to generate bisimplicial elimination schemes for bipartite graphs. Finally, we study two classes related to perfect disimplicial elimination digraphs, namely weakly diclique irreducible digraphs and diclique irreducible digraphs. The former class is associated to finite posets, while the latter corresponds to dedekind complete finite posets.

Solution to a problem of C. D. Godsil regarding bipartite graphs with unique perfect matching

COMBINATORICA ◽  
1989 ◽  
Vol 9 (1) ◽  
pp. 85-89 ◽  
Author(s):  
R. Simion ◽  
D. -S. Cao
Keyword(s):  
Perfect Matching ◽  
Bipartite Graphs

scholarly journals A perfect matching algorithm for sparse bipartite graphs

1984 ◽  
Vol 9 (3) ◽  
pp. 263-268
Author(s):  
Eugeniusz Toczyłowski
Keyword(s):  
Perfect Matching ◽  
Bipartite Graphs ◽  
Matching Algorithm

scholarly journals Perfect Matching Preservers

10.37236/1121 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Richard A. Brualdi ◽  
Martin Loebl ◽  
Ondřej Pangrác
Keyword(s):  
Perfect Matching ◽  
Bipartite Graphs

For two bipartite graphs $G$ and $G'$, a bijection $\psi: E(G) \rightarrow E(G')$ is called a (perfect) matching preserver provided that $M$ is a perfect matching in $G$ if and only if $\psi(M)$ is a perfect matching in $G'$. We characterize bipartite graphs $G$ and $G'$ which are related by a matching preserver and the matching preservers between them.

scholarly journals Upper paired domination in graphs

2021 ◽  
Vol 7 (1) ◽  
pp. 1185-1197
Author(s):  
Huiqin Jiang ◽  
◽  
Pu Wu ◽  
Jingzhong Zhang ◽  
Yongsheng Rao ◽  
...  
Keyword(s):  
Perfect Matching ◽  
Dominating Set ◽  
Bipartite Graphs ◽  
Proper Subset ◽  
Maximum Cardinality ◽  
Paired Domination ◽  
Domination In Graphs

<abstract><p>A set $ PD\subseteq V(G) $ in a graph $ G $ is a paired dominating set if every vertex $ v\notin PD $ is adjacent to a vertex in $ PD $ and the subgraph induced by $ PD $ contains a perfect matching. A paired dominating set $ PD $ of $ G $ is minimal if there is no proper subset $ PD'\subset PD $ which is a paired dominating set of $ G $. A minimal paired dominating set of maximum cardinality is called an upper paired dominating set, denoted by $ \Gamma_{pr}(G) $-set. Denote by $ Upper $-$ PDS $ the problem of computing a $ \Gamma_{pr}(G) $-set for a given graph $ G $. Michael et al. showed the APX-completeness of $ Upper $-$ PDS $ for bipartite graphs with $ \Delta = 4 $ <sup>[<xref ref-type="bibr" rid="b11">11</xref>]</sup>. In this paper, we show that $ Upper $-$ PDS $ is APX-complete for bipartite graphs with $ \Delta = 3 $.</p></abstract>

Perfect Matching Robustness of Balanced Bipartite Graphs

2012 ◽  
Vol 4 (20) ◽  
pp. 259-267
Author(s):  
Renfeng Xu ◽  
Yueping Li ◽  
Zhe Nie ◽  
Xiaojun Wen ◽  
Zhengxing Xiao
Keyword(s):  
Perfect Matching ◽  
Bipartite Graphs
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