Matchings in Graphs of Odd Regularity and Girth

Petersen proved that every 3-regular brigdeless graph has a perfect matching. Motivated by this result, several authors established lower bounds on the matching number of a graph subject to degree and girth conditions. In 2012 Henning et al. proved such a lower bound for connected 3-regular graphs....

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Bibliographic Details
Published inElectronic notes in discrete mathematics Vol. 44; pp. 3 - 8
Main Authors Costa, Vitor, Dantas, Simone, Rautenbach, Dieter
Format Journal Article
LanguageEnglish
Published Elsevier B.V 05.11.2013
Subjects
Matching
odd girth
regular graph
Matching
regular graph
odd girth
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Summary:Petersen proved that every 3-regular brigdeless graph has a perfect matching. Motivated by this result, several authors established lower bounds on the matching number of a graph subject to degree and girth conditions. In 2012 Henning et al. proved such a lower bound for connected 3-regular graphs. In the present paper, we extend their result by establishing lower bounds on the matching number of graphs of given odd regularity d and odd girth g, which are sharp for many values of d and g. For d=g=5, we characterize all extremal graphs.
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2013.10.002