# Isomorphism testing and canonical forms for k-contractable graphs (A generalization of bounded valence and bounded genus)

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## 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 Γ_{k} actions. It considers the canonical intersection of groups.

## Keywords

Canonical Form Permutation Group Wreath Product Multiple Edge Recursive Call
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## Copyright information

© Springer-Verlag Berlin Heidelberg 1983