P-Components and the Homogeneous Decomposition of Graphs

Authors:
Beverly Jamison;Stephan Olariu
Affiliations:
-;-
Venue:
SIAM Journal on Discrete Mathematics
Year:
1995

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Abstract

In this paper we introduce and investigate the notion of p-connectedness. As it turns out, this concept leads naturally to a unique tree representation for arbitrary graphs: the leaves of this tree are the p-connected components along with weak vertices, that is, vertices of the graph that belong to no p-connected component. We then show how to refine this decomposition to obtain a new decomposition that extends the well-known modular decomposition.