Abstract
This paper includes polynomial time isomorphism tests and canonical forms for graphs called k-contractable graphs for fixed k. The class of k-contractable graphs includes the graphs of bounded valence and the graphs of bounded genus. The algorithm uses several new ideas including: (1) it removes portions of the graph and replaces them with groups which are used to keep track of the symmetries of these portions; (2) it maintains with each group a tower of equivalence relation which allows a decomposition of the group. These towers are called a tower of Γk actions. It considers the canonical intersection of groups.
This work partially supported by NSF Grant MCS 800756-A01.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Bibliography
L. Babai, "Moderately Exponential Bound for Graph Isomorphism", Proc. Conf. on Foundation of Computation Theory, Szeget (1981).
L. Babai, P.J. Cameron, P.P. Palfy, "On the Order of Primitive Permutation Groups with Bounded Nonabelian Composition Factors", in preparation.
L. Babai, E. Luks, "Canonical Labeling of Graphs", STOC 83.
P.J. Cameron, "Finite Permutation Groups and Finite Simple Groups", Bull. London Math. Soc. 13, 1981, pp. 1–22.
I.S. Filotti, J.N. Mayer, "A Polynomial-time Algorithm for Determining the Isomorphism of Graphs of Fixed Genus", Proc. 12th ACM Symp. Th. Comp. (1980), pp. 236–243.
I.S. Filotti, G.L. Miller and J. Reif, "On Determining the Genus of a Graph in 0(V0(g)) Steps".
Furer, Schnyder, Specker, "Normal Forms for Frivalent Graphs", STOC 83.
J.E. Hopcroft, R.E. Tarjan, "Dividing a Graph into Triconnected Components", SIAM J. Comput., Vol. 2, No. 3, Sept. 1973, pp. 294–303.
D. Lichtenstein, "Isomorphism for Graphs Embeddable on the Projective Plane", Proc. 12th ACM Symp. Th. Symp. (1980), pp. 218–224.
E.M. Luks, "Isomorphism of Bounded Valence can be Tested in Polynomial Time", in Proc. 21st Annual Symposium of Foundations of Computer Science, IEEE (1980).
G.L. Miller, "Graph Isomorphism, General Remarks", JCSS, Vol. 18, No. 2, April 1979, pp. 128–141.
G.L. Miller, "Isomorphism Testing for Graphs of Bounded Genus" (working paper), Proc. 12th ACM Symp. Th. Comp. (1980), pp. 225–235.
G.L. Miller, "Isomorphism of Graphs which are Pairwise k-Separable", submitted to Information and Control.
G.L. Miller, "Isomorphism of k-Contractable Graphs (a generalization of bounded valence and bounded genus)", submitted to Information and Control.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1983 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Miller, G.L. (1983). Isomorphism testing and canonical forms for k-contractable graphs (A generalization of bounded valence and bounded genus). In: Karpinski, M. (eds) Foundations of Computation Theory. FCT 1983. Lecture Notes in Computer Science, vol 158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12689-9_114
Download citation
DOI: https://doi.org/10.1007/3-540-12689-9_114
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12689-8
Online ISBN: 978-3-540-38682-7
eBook Packages: Springer Book Archive