Induced-path partition on graphs with special blocks

Authors:
Jun-Jie Pan;Gerard J. Chang
Affiliations:
Department of Mathematics, Fu Jen Catholic University, 510 Chung Cheng Road, Hsinchuang, Taipei Hsien 24205, Taiwan;Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan and Taida Institute for Mathematical Sciences, National Taiwan University, Taipei 10617, Taiwan and National Center for ...
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

In a graph, an induced path is a path v"0,v"1,...,v"r in which a vertex v"i is adjacent to another vertex v"j if and only if |i-j|=1. An induced-path partition of a graph is a collection of vertex-disjoint induced paths that cover all vertices of the graph. The induced-path-partition problem is to determine the minimum cardinality of an induced-path partition of a graph. This paper presents an O(|V|+|E|)-time algorithm for the induced-path-partition problem on graphs whose blocks are complete graphs, cycles or complete bipartite graphs.