Algorithms for the Minimum Edge Cover of H-Subgraphs of a Graph

A. Grigoriev*, L. Marchal, N. Usotskaya

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review


We consider the following problem: given graph G and a set of graphs H = {H-1,...,H-i} what is the smallest subset S of edges in G such that all subgraphs of G that are isomorphic to one of the graphs from H contain at least one edge from S? Equivalently, we aim to find the minimum number of edges that needs to be removed from G to make it H-free. We concentrate on the case where all graphs H-i are connected and have fixed size. Several algorithmic results are presented. First, we derive a polynomial time dynamic program for the problem on graphs of bounded treewidth and bounded maximum vertex degree. Then, if H contains only a clique, we adjust the dynamic program to solve the problem on graphs of bounded treewidth having arbitrary maximum vertex degree. Using the constructed dynamic programs, we design a Baker's type approximation scheme for the problem on planar graphs. Finally, we observe that our results hold also if we cover only induced H-subgraphs.
Original languageEnglish
Title of host publicationTheory and Practice of Computer Science
EditorsJ. van Leeuwen
Place of PublicationBerlin / Heidelberg
Number of pages13
Publication statusPublished - 1 Jan 2010

Publication series

SeriesLecture Notes in Computer Science


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