Chen, Xuegang and Huang, Jing - Uniquely monopolar-partitionable block graphs

dmtcs:2073 - Discrete Mathematics & Theoretical Computer Science, May 6, 2014, Vol. 16 no. 2
Uniquely monopolar-partitionable block graphs

Authors: Chen, Xuegang and Huang, Jing

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.

Volume: Vol. 16 no. 2
Section: PRIMA 2013
Published on: May 6, 2014
Submitted on: December 27, 2013
Keywords: Monopolar graph,monopolar partition,uniquely monopolar-partitionable grap,block graph,characterization,polynomial time algorithm,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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