Fast Algorithms forK4Immersion Testing

Many useful classes of graphs can in principle be recognized with finite batteries of obstruction tests. One of the most fundamental tests is to determine whether an arbitrary input graph contains K4 in the immersion order. In this paper, we present for the first time a fast, practical algorithm to accomplish this task. We also extend our method so that, should an immersed K4 be present, a K4 model is isolated. ∗ This research has been supported in part by the National Science Foundation under grant CDA–9115428 and by the Office of Naval Research under contract N00014–90–J–1855. † A preliminary version of a portion of this paper was presented at the Great Lakes Symposium on VLSI, held in Kalamazoo, Michigan, in February, 1992. 1 Department of Computer Science, University of Tennessee, Knoxville, TN 37996. 2 Qualcomm Incorporated, San Diego, CA 92121. 3 LSI Logic Corporation, Waltham, MA 02451.