Abstract

A structure theorem is proved for the class of graphs of bounded average genus, which leads to a linear-time algorithm for isomorphism of such graphs.

MSC codes

  1. 05C10
  2. 05C60
  3. 05C85
  4. 57M15
  5. 68R10

Keywords

  1. algorithm
  2. graph isomorphism
  3. graph imbedding

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References

1.
Jianer Chen, A linear time algorithm for isomorphism of graphs of bounded average genusGraph-theoretic concepts in computer science (Wiesbaden-Naurod, 1992), Lecture Notes in Comput. Sci., Vol. 657, Springer, Berlin, 1993, 103–113
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Jianer Chen, Jonathan L. Gross, Limit points for average genus. I. 3-connected and 2-connected simplicial graphs, J. Combin. Theory Ser. B, 55 (1992), 83–103
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Jianer Chen, Jonathan L. Gross, Limit points for average genus. II. 2-connected nonsimplicial graphs, J. Combin. Theory Ser. B, 56 (1992), 108–129
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Jianer Chen, Jonathan L. Gross, Kuratowski-type theorems for average genus, J. Combin. Theory Ser. B, 57 (1993), 100–121
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I. S. Filotti, J. N. Mayer, A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus, Proc. 12th Annual ACM Symposium on Theory of Comput., Los Angeles, CA, 1980, 236–243, April
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Jonathan L. Gross, Merrick L. Furst, Hierarchy for imbedding-distribution invariants of a graph, J. Graph Theory, 11 (1987), 205–220
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Jonathan L. Gross, E. Ward Klein, Robert G. Rieper, On the average genus of a graph, Graphs Combin., 9 (1993), 153–162
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Richard D. Ringeisen, Determining all compact orientable 2-manifolds upon which $K\sb {m,\, n}$ has 2-cell imbeddings, J. Combinatorial Theory Ser. B, 12 (1972), 101–104
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Information

Published In

cover image SIAM Journal on Discrete Mathematics
SIAM Journal on Discrete Mathematics
Pages: 614 - 631
ISSN (online): 1095-7146

History

Submitted: 18 March 1991
Accepted: 16 July 1993
Published online: 17 February 2012

MSC codes

  1. 05C10
  2. 05C60
  3. 05C85
  4. 57M15
  5. 68R10

Keywords

  1. algorithm
  2. graph isomorphism
  3. graph imbedding

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