The cost of perfection for matchings in graphs

Perfect matchings and maximum weight matchings are two fundamental combinatorial structures. We consider the ratio between the maximum weight of a perfect matching and the maximum weight of a general matching. Motivated by the computer graphics application in triangle meshes, where we seek to conver...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 210; pp. 112 - 122
Main Authors Brazil, E.V., de Figueiredo, C.M.H., da Fonseca, G.D., Sasaki, D.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 10.09.2016
Subjects
Combinatorial analysis
Cubic graphs
Graphs
Lower bounds
Matching
Mathematical models
Merging
Perfect matchings
Regular bipartite graphs
Triangle meshes
Triangles
Upper bounds
Triangle meshes
Cubic graphs
Perfect matchings
Regular bipartite graphs
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Summary:Perfect matchings and maximum weight matchings are two fundamental combinatorial structures. We consider the ratio between the maximum weight of a perfect matching and the maximum weight of a general matching. Motivated by the computer graphics application in triangle meshes, where we seek to convert a triangulation into a quadrangulation by merging pairs of adjacent triangles, we focus mainly on bridgeless cubic graphs. First, we characterize graphs that attain the extreme ratios. Second, we present a lower bound for all bridgeless cubic graphs. Third, we present upper bounds for subclasses of bridgeless cubic graphs, most of which are shown to be tight. Additionally, we present tight bounds for the class of regular bipartite graphs.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2014.12.006