14 research outputs found
Chordless Cycle Packing Is Fixed-Parameter Tractable
A chordless cycle or hole in a graph G is an induced cycle of length at least 4. In the Hole Packing problem, a graph G and an integer k is given, and the task is to find (if exists) a set of k pairwise vertex-disjoint chordless cycles. Our main result is showing that Hole Packing is fixed-parameter tractable (FPT), that is, can be solved in time f(k)n^O(1) for some function f depending only on k
Preprocessing Subgraph and Minor Problems: When Does a Small Vertex Cover Help?
We prove a number of results around kernelization of problems parameterized
by the size of a given vertex cover of the input graph. We provide three sets
of simple general conditions characterizing problems admitting kernels of
polynomial size. Our characterizations not only give generic explanations for
the existence of many known polynomial kernels for problems like q-Coloring,
Odd Cycle Transversal, Chordal Deletion, Eta Transversal, or Long Path,
parameterized by the size of a vertex cover, but also imply new polynomial
kernels for problems like F-Minor-Free Deletion, which is to delete at most k
vertices to obtain a graph with no minor from a fixed finite set F.
While our characterization captures many interesting problems, the
kernelization complexity landscape of parameterizations by vertex cover is much
more involved. We demonstrate this by several results about induced subgraph
and minor containment testing, which we find surprising. While it was known
that testing for an induced complete subgraph has no polynomial kernel unless
NP is in coNP/poly, we show that the problem of testing if a graph contains a
complete graph on t vertices as a minor admits a polynomial kernel. On the
other hand, it was known that testing for a path on t vertices as a minor
admits a polynomial kernel, but we show that testing for containment of an
induced path on t vertices is unlikely to admit a polynomial kernel.Comment: To appear in the Journal of Computer and System Science
Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization
International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
LIPIcs, Volume 244, ESA 2022, Complete Volume
LIPIcs, Volume 244, ESA 2022, Complete Volum