Isomorphism of k-contractible graphs. A generalization of bounded valence and bounded genus

Gary L. Miller
1983 Information and Control  
A polynomial time isomorphism test for graphs called k-contractible graphs for fixed k is included. The class of k-contractible 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 relations which allow a decomposition of the group. These towers are called towers of Fk-actions.
doi:10.1016/s0019-9958(83)80047-3 fatcat:7hvtd2q4tnfn5drybtgqnxvvjm