Finding the maximum common subgraph of a partial k-tree and a graph with a polynomially bounded number of spanning trees

Abstract

The maximum common subgraph problem is NP-hard even if the two input graphs are partial k-trees. We present a polynomial time algorithm for finding the maximum common connected induced subgraph of two bounded degree graphs G1 and G2, where G1 is a partial k-tree and G2 is a graph whose possible spanning trees are polynomially bounded. The key idea of our algorithm is that for each spanning tree generated from G2, a candidate for the maximum common connected induced subgraph is generated in polynomial time since a subgraph of a partial k-tree is also a partial k-tree. Among all of these candidates, we can find the maximum common connected induced subgraph for G1 and G2. © Springer-Verlag Berlin Heidelberg 2003.