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Published in:
2012 | OriginalPaper | Chapter
k-Gap Interval Graphs
Authors : Fedor V. Fomin, Serge Gaspers, Petr Golovach, Karol Suchan, Stefan Szeider, Erik Jan van Leeuwen, Martin Vatshelle, Yngve Villanger
Published in: LATIN 2012: Theoretical Informatics
Publisher: Springer Berlin Heidelberg
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We initiate the study of a new parameterization of graph problems. In a multiple interval representation of a graph, each vertex is associated to at least one interval of the real line, with an edge between two vertices if and only if an interval associated to one vertex has a nonempty intersection with an interval associated to the other vertex. A graph on
n
vertices is a
k
-gap interval graph if it has a multiple interval representation with at most
n
+
k
intervals in total. In order to scale up the nice algorithmic properties of interval graphs (where
k
= 0), we parameterize graph problems by
k
, and find FPT algorithms for several problems, including
Feedback Vertex Set
,
Dominating Set
,
Independent Set
,
Clique
,
Clique Cover
, and
Multiple Interval Transversal
. The
Coloring
problem turns out to be
-hard and we design an XP algorithm for the recognition problem.