eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-11-28
16:1
16:13
10.4230/LIPIcs.ISAAC.2019.16
article
Cyclability in Graph Classes
Crespelle, Christophe
1
Feghali, Carl
1
Golovach, Petr A.
1
Department of Informatics, University of Bergen, Norway
A subset T subseteq V(G) of vertices of a graph G is said to be cyclable if G has a cycle C containing every vertex of T, and for a positive integer k, a graph G is k-cyclable if every subset of vertices of G of size at most k is cyclable. The Terminal Cyclability problem asks, given a graph G and a set T of vertices, whether T is cyclable, and the k-Cyclability problem asks, given a graph G and a positive integer k, whether G is k-cyclable. These problems are generalizations of the classical Hamiltonian Cycle problem. We initiate the study of these problems for graph classes that admit polynomial algorithms for Hamiltonian Cycle. We show that Terminal Cyclability can be solved in linear time for interval graphs, bipartite permutation graphs and cographs. Moreover, we construct certifying algorithms that either produce a solution, that is, a cycle, or output a graph separator that certifies a no-answer. We use these results to show that k-Cyclability can be solved in polynomial time when restricted to the aforementioned graph classes.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol149-isaac2019/LIPIcs.ISAAC.2019.16/LIPIcs.ISAAC.2019.16.pdf
Cyclability
interval graphs
bipartite permutation graphs
cographs