@InProceedings{LPR78, replaced-by = { LPR80 }, author = { Andrea S. LaPaugh and Ronald L. Rivest }, title = { The subgraph homeomorphism problem }, pages = { 40--50 }, url = { http://doi.acm.org/10.1145/800133.804330 }, doi = { 10.1145/800133.804330 }, acmid = { 804330 }, acm = { 08117 }, booktitle = { Proceedings of the tenth annual ACM symposium on Theory of computing }, date = { 1978 }, publisher = { ACM }, editor = { Richard J. Lipton }, OPTyear = { 1978 }, OPTmonth = { May 1--3, }, eventdate = { 1978-05-01/1978-05-03 }, eventtitle = { STOC '78 }, venue = { San Diego, California }, OPTorganization = { ACM }, 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. }, }