research-article

Random Graph Isomorphism

Authors:

László Babai,

Paul Erdo˝s,

Stanley M. SelkowAuthors Info & Claims

SIAM Journal on Computing, Volume 9, Issue 3

Pages 628 - 635

https://doi.org/10.1137/0209047

Published: 01 August 1980 Publication History

Abstract

A straightforward linear time canonical labeling algorithm is shown to apply to almost all graphs (i.e. all but $o(2^{( \begin{subarray}{l} n \\ 2 \end{subarray} )} )$) of the $2^{( \begin{subarray}{l} n \\ 2 \end{subarray} )} $ graphs on n vertices). Hence, for almost all graphs X, any graph Y can be easily tested for isomorphism to X by an extremely naive linear time algorithm. This result is based on the following: In almost all graphs on n vertices, the largest $n^{0.15} $ degrees are distinct. In fact, they are pairwise at least $n^{0.03} $ apart.

References

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P. Erdös, Robin J. Wilson, On the chromatic index of almost all graphs, J. Combinatorial Theory Ser. B, 23 (1977), 255–257

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Index Terms

Random Graph Isomorphism
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Graph enumeration
2. Theory of computation
  1. Design and analysis of algorithms
  2. Randomness, geometry and discrete structures

Index terms have been assigned to the content through auto-classification.

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Published In

SIAM Journal on Computing Volume 9, Issue 3

Aug 1980

224 pages

ISSN:0097-5397

DOI:10.1137/smjcat.1980.9.issue-3

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 August 1980

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Hershko TZhukovskii MSobocinski PLago UEsparza J(2024)First order distinguishability of sparse random graphsProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662117(1-14)Online publication date: 8-Jul-2024
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Recommendations

Improved random graph isomorphism

Regular induced subgraphs of a random Graph

Some forbidden subgraph conditions for a graph to have a k-contractible edge

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