Bicolored Matchings in Some Classes of Graphs
Published in:
 Graphs and Combinatorics.  2007, vol. 23, no. 1, p. 4760
English
We consider the problem of finding in a graph a set R of edges to be colored in red so that there are maximum matchings having some prescribed numbers of red edges. For regular bipartite graphs with n nodes on each side, we give sufficient conditions for the existence of a set R with R = n + 1 such that perfect matchings with k red edges exist for all k, 0 ≤ k ≤ n. Given two integers p < q we also determine the minimum cardinality of a set R of red edges such that there are perfect matchings with p red edges and with q red edges. For 3regular bipartite graphs, we show that if p ≤ 4 there is a set R with R = p for which perfect matchingsMk exist with Mk ∩R ≤ k for all k ≤ p. For trees we design a linear time algorithm to determine a minimum set R of red edges such that there exist maximum matchings with k red edges for the largest possible number of values of k.

Faculty
 Faculté des sciences économiques et sociales et du management

Department
 Département d'informatique

Language


Classification

Computer science and technology

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https://folia.unifr.ch/unifr/documents/307835
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