A POLYNOMIAL-TIME ALGORITHM FOR FINDING A LARGEST COMMON SUBGRAPH OF ALMOST TREES OF BOUNDED DEGREE

This paper considers the problem of finding a largest common subgraph of graphs, which is an important problem in chemical synthesis. It is known that the problem is NP-hard even if graphs are restricted to planar graphs of vertex degree at most three. By the way, a graph is called an almost tree if \E (B)\ less-than-or-equal-to \V (B)\ + K holds for every block B where K is a constant. In this paper, a polynomial time algorithm for finding a largest common subgraph of two graphs which are connected, almost trees and of bounded vertex degree. The algorithm is an extension of a subtree isomorphism algorithm which is based on dynamic programming. Moreover, it is shown that the degree bound is essential. That is, the problem of finding a largest common subgraph of two connected almost trees is proved to be NP-hard for any K greater-than-or-equal-to 0 if degree is not bounded. The three dimensional matching problem, a well known NP-complete problem, is reduced to the problem.