Abstract
We consider the following problem: given graph G and a set of graphs H = {H 1,...,H t }, 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.
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Grigoriev, A., Marchal, B., Usotskaya, N. (2010). Algorithms for the Minimum Edge Cover of H-Subgraphs of a Graph. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11266-9_38
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DOI: https://doi.org/10.1007/978-3-642-11266-9_38
Publisher Name: Springer, Berlin, Heidelberg
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