The 1-Fixed-Endpoint Path Cover Problem is Polynomial on Interval Graphs (Journal article)

Asdre, K./ Nikolopoulos, S. D.

We consider a variant of the path cover problem, namely, the k-fixed-endpoint 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: 4964, 1993), where he left both 1HP and 2HP problems open for the class of interval graphs, we show that the 1PC problem can be solved in polynomial time on the class of interval graphs. We propose a polynomial-time algorithm for the problem, which also enables us to solve the 1HP problem on interval graphs within the same time and space complexity.
Institution and School/Department of submitter: Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μηχανικών Ηλεκτρονικών Υπολογιστών και Πληροφορικής
Keywords: perfect graphs,interval graphs,path cover,fixed-endpoint path cover,linear-time algorithms,distance-hereditary graphs,finding hamiltonian circuits,circular-arc graphs,disjoint paths,algorithm,cographs
ISSN: 0178-4617
Appears in Collections:Άρθρα σε επιστημονικά περιοδικά ( Ανοικτά)

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