The 1-Fixed-Endpoint Path Cover Problem is Polynomial on Interval Graphs

Abstract We consider a variant of the path cover problem, namely, the k-fixedendpoint path cover problem, or kPC for short, on interval graphs. Given a graph G and a subset T of k vertices of V (G), a k-fixed-endpoint path cover of G with respect to T is a set of vertex-disjoint paths P that covers the vertices of G such that the k vertices of T are all endpoints of the paths in P. The kPC problem is to find a k-fixed-endpoint path cover of G of minimum cardinality; note that, if T is empty the stated problem coincides with the classical path cover problem. In this paper, we study the 1-fixed-endpoint path cover problem on interval graphs, or 1PC for short, generalizing the 1HP problem which has been proved to be NP-complete even for small classes of graphs. Motivated by a work of Damaschke (Discrete Math. 112:49

• Type: Journal
• Year: 2010
• Where: ALGORITHMICA
• Authors: Katerina Asdre, Stavros D. Nikolopoulos
• Keywords: ALGORITHMICA 2010, Interval Graphs, K-fixed-endpoint Path Cover, K-fixedendpoint Path