A linear time algorithm for isomorphism of graphs of bounded average genus
Recent progress in topological graph theory has shown potential applicability of average genus to graph isomorphism testing. The present paper describes an initial effort at combining topological invariants with combinatorial analysis to design efficient graph isomorphism algorithms. In particular, a linear time algorithm for isomorphism of graphs of bounded average genus is presented.
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- 1.Chen, J.: A linear time algorithm for isomorphism of graphs of bounded average genus. Technical Report 91-015, Dept. of Computer Science, Texas A&M University (1991)Google Scholar
- 2.Chen, J., Gross, J. L.: Limit points for average genus (I): 3-connected and 2-connected simplicial graphs. J. Comb. Theory Ser. B 55 (1992) 83–103Google Scholar
- 3.Chen, J., Gross, J. L.: Limit points for average genus (II): 2-connected non-simplicial graphs. J. Comb. Theory Ser. B (to appear)Google Scholar
- 4.Chen, J., Gross, J. L.: Kuratowski-type theorem for average genus. J. Comb. Theory Ser. B (to appear)Google Scholar
- 5.Chen, J., Gross, J. L.: No lower limit points for average genus. Graph Theory, Combinatorics, Algorithms, and Applications, Ed. Alavi and others, Wiley Interscience (to appear)Google Scholar
- 6.Filotti, I. S., Mayer, J. N.: A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus. Proc. 12th Annual ACM Symposium on Theory of Computing (1980) 236–243Google Scholar
- 7.Gross, J. L., Furst, M. L.: Hierarchy for imbedding-distribution invariants of a graph. J. Graph Theory 11 (1987) 205–220Google Scholar
- 8.Gross, J. L., Tucker, T. W.: Topological Graph Theory, Wiley-Interscience, New York (1987)Google Scholar
- 9.Hopcroft, J. E., Wong, J. K.: Linear time algorithm for isomorphism of planar graphs. Proc. 6th Annual ACM Symposium on Theory of Computing (1974) 172–184Google Scholar
- 10.Ramachandran, V.: Parallel open ear decomposition with applications to graph biconnectivity and triconnectivity. Synthesis of Parallel Algorithms, Ed. Reif, MorganKaufmann (to appear)Google Scholar
- 11.Tutte, W. T.: Connectivity in Graphs, University of Toronto Press (1966)Google Scholar
- 12.Tutte, W. T.: Graph Theory. Addison-Wesley Publishing Company (1984)Google Scholar
- 13.Whitney, H.: Non-separable and planar graphs. Trans. Amer. Math. Soc. 34 (1932) 339–362Google Scholar