scholarly journals Finding all the perfect matchings in bipartite graphs

1994 ◽  
Vol 7 (1) ◽  
pp. 15-18 ◽  
Author(s):  
K. Fukuda ◽  
T. Matsui
Keyword(s):  
Bipartite Graphs ◽  
Perfect Matchings

scholarly journals Perfect Matchings in Õ (n1.5) Time in Regular Bipartite Graphs

COMBINATORICA ◽  
2018 ◽  
Vol 39 (2) ◽  
pp. 323-354
Author(s):  
Ashish Goel ◽  
Michael Kapralov ◽  
Sanjeev Khanna
Keyword(s):  
Bipartite Graphs ◽  
Perfect Matchings

scholarly journals Bipartite Graphs Associated with Pell, Mersenne and Perrin Numbers

2019 ◽  
Vol 27 (2) ◽  
pp. 109-120
Author(s):  
Ahmet Öteleş
Keyword(s):  
Bipartite Graphs ◽  
Perfect Matchings

AbstractIn this paper, we consider the relationships between the numbers of perfect matchings (1-factors) of bipartite graphs and Pell, Mersenne and Perrin Numbers. Then we give some Maple procedures in order to calculate the numbers of perfect matchings of these bipartite graphs.

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 A Graph Polynomial for Independent Sets of Bipartite Graphs

2012 ◽  
Vol 21 (5) ◽  
pp. 695-714 ◽  
Author(s):  
Q. GE ◽  
D. ŠTEFANKOVIČ
Keyword(s):  
Riemann Hypothesis ◽  
Independent Sets ◽  
Bipartite Graphs ◽  
Rational Points ◽  
Perfect Matchings ◽  
Generalized Riemann Hypothesis ◽  
Graph Polynomial ◽  
Exact Evaluation

We introduce a new graph polynomial that encodes interesting properties of graphs, for example, the number of matchings, the number of perfect matchings, and, for bipartite graphs, the number of independent sets (#BIS).We analyse the complexity of exact evaluation of the polynomial at rational points and show a dichotomy result: for most points exact evaluation is #P-hard (assuming the generalized Riemann hypothesis) and for the rest of the points exact evaluation is trivial.

scholarly journals Perfect Matchings in $O(n\log n)$ Time in Regular Bipartite Graphs

2013 ◽  
Vol 42 (3) ◽  
pp. 1392-1404 ◽  
Author(s):  
Ashish Goel ◽  
Michael Kapralov ◽  
Sanjeev Khanna
Keyword(s):  
Bipartite Graphs ◽  
Perfect Matchings

Finding all minimum-cost perfect matchings in Bipartite graphs

Networks ◽  
1992 ◽  
Vol 22 (5) ◽  
pp. 461-468 ◽  
Author(s):  
Komei Fukuda ◽  
Tomomi Matsui
Keyword(s):  
Minimum Cost ◽  
Bipartite Graphs ◽  
Perfect Matchings

scholarly journals Matchings in Random Biregular Bipartite Graphs

10.37236/2658 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Guillem Perarnau ◽  
Giorgis Petridis
Keyword(s):  
Number Theory ◽  
Bipartite Graphs ◽  
Perfect Matchings ◽  
Additive Number Theory ◽  
Classical Theorem ◽  
Induced Subgraphs ◽  
Additive Number

We study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdös and Rényi about perfect matchings in random bipartite graphs. We also present an application to commutative graphs, a class of graphs that are featured in additive number theory.

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