scholarly journals Cubic graphs that cannot be covered with four perfect matchings

2021 ◽  
Vol 150 ◽  
pp. 144-176
Author(s):  
Edita Máčajová ◽  
Martin Škoviera
Keyword(s):  
Perfect Matchings ◽  
Cubic Graphs

scholarly journals The Fan–Raspaud conjecture: A randomized algorithmic approach and application to the pair assignment problem in cubic networks

2012 ◽  
Vol 22 (3) ◽  
pp. 765-778
Author(s):  
Piotr Formanowicz ◽  
Krzysztof Tanaś
Keyword(s):  
Graph Theory ◽  
Computer Networks ◽  
Assignment Problem ◽  
Perfect Matchings ◽  
Cubic Graphs ◽  
Cubic Graph ◽  
Algorithmic Approach ◽  
Edge Colorings ◽  
Mathematical Properties

Abstract It was conjectured by Fan and Raspaud (1994) that every bridgeless cubic graph contains three perfect matchings such that every edge belongs to at most two of them. We show a randomized algorithmic way of finding Fan–Raspaud colorings of a given cubic graph and, analyzing the computer results, we try to find and describe the Fan–Raspaud colorings for some selected classes of cubic graphs. The presented algorithms can then be applied to the pair assignment problem in cubic computer networks. Another possible application of the algorithms is that of being a tool for mathematicians working in the field of cubic graph theory, for discovering edge colorings with certain mathematical properties and formulating new conjectures related to the Fan–Raspaud conjecture.

A CHARACTERIZATION OF PM-COMPACT CLAW-FREE CUBIC GRAPHS

2014 ◽  
Vol 06 (02) ◽  
pp. 1450025 ◽  
Author(s):  
XIUMEI WANG ◽  
WEIPING SHANG ◽  
YIXUN LIN ◽  
MARCELO H. CARVALHO
Keyword(s):  
Convex Hull ◽  
Perfect Matching ◽  
Perfect Matchings ◽  
Cubic Graphs ◽  
Matching Polytopes ◽  
Matching Polytope

The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings in G. This paper characterizes claw-free cubic graphs whose 1-skeleton graphs of perfect matching polytopes have diameter 1.

Unions of perfect matchings in cubic graphs

2005 ◽  
Vol 22 ◽  
pp. 341-345 ◽  
Author(s):  
Tomáš Kaiser ◽  
Daniel Král' ◽  
Serguei Norine
Keyword(s):  
Perfect Matchings ◽  
Cubic Graphs

scholarly journals Perfect Matching Covers of Cubic Graphs of Oddness 2

10.37236/7175 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Wuyang Sun ◽  
Fan Wang
Keyword(s):  
Perfect Matching ◽  
Perfect Matchings ◽  
Cubic Graphs ◽  
Cubic Graph

A perfect matching cover of a graph $G$ is a set of perfect matchings of $G$ such that each edge of $G$ is contained in at least one member of it. Berge conjectured that every bridgeless cubic graph has a perfect matching cover of order at most 5. The Berge Conjecture is largely open and it is even unknown whether a constant integer $c$ does exist such that every bridgeless cubic graph has a perfect matching cover of order at most $c$. In this paper, we show that a bridgeless cubic graph $G$ has a perfect matching cover of order at most 11 if $G$ has a 2-factor in which the number of odd circuits is 2.

scholarly journals Perfect Matchings in Claw-free Cubic Graphs

10.37236/549 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Sang-il Oum
Keyword(s):  
Positive Constant ◽  
Planar Graphs ◽  
Bipartite Graphs ◽  
Perfect Matchings ◽  
Cubic Graphs ◽  
Vertex Graph

Lovász and Plummer conjectured that there exists a fixed positive constant $c$ such that every cubic $n$-vertex graph with no cutedge has at least $2^{cn}$ perfect matchings. Their conjecture has been verified for bipartite graphs by Voorhoeve and planar graphs by Chudnovsky and Seymour. We prove that every claw-free cubic $n$-vertex graph with no cutedge has more than $2^{n/12}$ perfect matchings, thus verifying the conjecture for claw-free graphs.

scholarly journals A New Lower Bound on the Number of Perfect Matchings in Cubic Graphs

2009 ◽  
Vol 23 (3) ◽  
pp. 1465-1483 ◽  
Author(s):  
Daniel Král' ◽  
Jean-Sébastien Sereni ◽  
Michael Stiebitz
Keyword(s):  
Lower Bound ◽  
Perfect Matchings ◽  
Cubic Graphs

Sparsely intersecting perfect matchings in cubic graphs

COMBINATORICA ◽  
2014 ◽  
Vol 34 (1) ◽  
pp. 61-94 ◽  
Author(s):  
Edita Máčajová ◽  
Martin Škoviera
Keyword(s):  
Perfect Matchings ◽  
Cubic Graphs
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