Some results on graphs without long induced paths

Authors:
Vadim Lozin;Dieter Rautenbach
Affiliations:
RUTCOR, Rutgers University, 640 Bartholomew Rd, Piscataway, NJ;Forschungsinstitut für Diskrete Mathematik, Universität Bonn, 53113 Bonn, Germany
Venue:
Information Processing Letters
Year:
2003

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Abstract

Many NP-hard graph problems remain difficult on Pk-free graphs for certain values of k. Our goal is to distinguish subclasses of Pk-free graphs where several important graph problems can be solved in polynomial time. In particular, we show that the independent set problem is polynomial-time solvable in the class of (Pk, K1,n)-free graphs for any positive integers k and n, thereby generalizing several known results.