@Article{LPR80, author = { Andrea S. LaPaugh and Ronald L. Rivest }, title = { The Subgraph homeomorphism problem }, journal = { JCSS }, OPTyear = { 1980 }, OPTmonth = { April }, date = { 1980-04 }, volume = { 20 }, number = { 2 }, pages = { 133--149 }, issn = { 0022-0000 }, doi = { 10.1016/0022-0000(80)90057-4 }, url = { http://www.sciencedirect.com/science/article/pii/0022000080900574 }, abstract = { 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. }, }