License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2016.36
URN: urn:nbn:de:0030-drops-57370
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5737/
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Fomin, Fedor V. ; Golovach, Petr ; Panolan, Fahad ; Saurabh, Saket

Editing to Connected f-Degree Graph

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Abstract

In the EDGE EDITING TO CONNECTED f-DEGREE GRAPH problem we are given a graph G, an integer k and a function f assigning integers to vertices of G. The task is to decide whether there is a connected graph F on the same vertex set as G, such that for every vertex v, its degree in F is f(v) and the number of edges inthe symmetric difference of E(G) and E(F), is at most k. We show that EDGE EDITING TO CONNECTED f-DEGREE GRAPH is fixed-parameter tractable (FPT) by providing an algorithm solving the problem on an n-vertex graph in time 2^{O(k)}n^{O(1)}. Our FPT algorithm is based on a non-trivial combination of color-coding and fast computations of representative families over direct sum matroid of l-elongation of co-graphic matroid associated with G and uniform matroid over the set of non-edges of G. We believe that this combination could be useful in designing parameterized algorithms for other edge editing problems.

BibTeX - Entry

@InProceedings{fomin_et_al:LIPIcs:2016:5737,
  author =	{Fedor V. Fomin and Petr Golovach and Fahad Panolan and Saket Saurabh},
  title =	{{Editing to Connected f-Degree Graph}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{36:1--36:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Nicolas Ollinger and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5737},
  URN =		{urn:nbn:de:0030-drops-57370},
  doi =		{10.4230/LIPIcs.STACS.2016.36},
  annote =	{Keywords: Connected f-factor, FPT, Representative Family, Color Coding}
}

Keywords: Connected f-factor, FPT, Representative Family, Color Coding
Collection: 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Issue Date: 2016
Date of publication: 16.02.2016

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