Abstract : As a common generalization of bipartite and split graphs, monopolar graphs are defined in terms of the existence of certain vertex partitions. It has been shown that to determine whether a graph has such a partition is NP-complete for general graphs and polynomial for several classes of graphs. In this paper, we investigate graphs that admit a unique such partition and call them uniquely monopolar-partitionable graphs. By employing a tree trimming technique, we obtain a characterization of uniquely monopolar-partitionable block graphs. Our characterization implies a polynomial time algorithm for recognizing them.
https://hal.inria.fr/hal-01185613
Contributeur : Coordination Episciences Iam
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Soumis le : jeudi 20 août 2015 - 17:13:41
Dernière modification le : jeudi 7 septembre 2017 - 01:03:44
Document(s) archivé(s) le : mercredi 26 avril 2017 - 10:12:21
