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Editing to Connected f-Degree Graph

Authors Fedor V. Fomin, Petr Golovach, Fahad Panolan, Saket Saurabh

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Fedor V. Fomin
Petr Golovach
Fahad Panolan
Saket Saurabh

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Fedor V. Fomin, Petr Golovach, Fahad Panolan, and Saket Saurabh. Editing to Connected f-Degree Graph. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.STACS.2016.36

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.
Keywords
  • Connected f-factor
  • FPT
  • Representative Family
  • Color Coding

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