The subgraph homeomorphism problem

摘要

We investigate the problem of finding a homeomorphic image of a “pattern” graph H in a larger input graph G. We view this problem as finding specified sets of edge disjoint or node disjoint paths in G. Our main result is a linear time algorithm to determine if there exists a simple cycle containing three given nodes in G (here H is a triangle). No polynomial time algorithm for this problem was previously known. We also discuss a variety of reductions between related versions of this problem and a number of open problems.