Abstract
In this note a greedy algorithm is considered that computes a matching for a graph with a given ordering of its vertices, and those graphs are studied for which a vertex ordering exists such that the greedy algorithm always yields maximum cardinality matchings for each induced subgraph. We show that these graphs, called greedy matchable graphs, are a subclass of weakly triangulated graphs and contain strongly chordal graphs and chordal bipartite graphs as proper subclasses. The question when can this ordering be produced efficiently is discussed too.
Research supported by the VW, Project No. 1/69041, and by the DFG.
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© 1997 Springer-Verlag Berlin Heidelberg
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Dragan, F.F. (1997). On greedy matching ordering and greedy matchable graphs. In: Möhring, R.H. (eds) Graph-Theoretic Concepts in Computer Science. WG 1997. Lecture Notes in Computer Science, vol 1335. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024498
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DOI: https://doi.org/10.1007/BFb0024498
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