Efficient recognition of equimatchable graphs

Authors:
Marc Demange;Tınaz Ekim
Affiliations:
ESSEC Business School, Paris, France and LAMSADE UMR 7243, Paris, France;Boğaziçi University, Department of Industrial Engineering, Istanbul, Turkey
Venue:
Information Processing Letters
Year:
2014

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Abstract

In this paper, we give a new characterization of equimatchable graphs that are graphs with all maximal matchings having the same size. This gives an O(n^2m)-algorithm for deciding whether a general graph of order n and with m edges is equimatchable. An O(n^4^.^5) recognition algorithm based on the Gallai-Edmonds Decomposition already follows from Lesk et al. (1984) [8]. Our characterization and algorithm use only some basic knowledge on matchings and can be formulated in a simplier way. Moreover it leads to a better time complexity.