Finding the Maximum Common Subgraph of a Partial k-Tree and a Graph with a Polynomially Bounded Number of Spanning Trees
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.
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