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zbMATH Open
Article . 1980
Data sources: zbMATH Open
SIAM Journal on Computing
Article . 1980 . Peer-reviewed
Data sources: Crossref
DBLP
Article
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Random Graph Isomorphism

Random graph isomorphism
Authors: László Babai; Paul Erdös; Stanley M. Selkow;

Random Graph Isomorphism

Abstract

Summary: A straightforward linear time canonical labeling algorithm is shown to apply to almost all graphs (i.e. all but \(O(2^{\binom n2})\) of the \(2^{\binom n2})\) graphs on \(n\) vertices). Hence, for almost all graphs \(X\), and graph \(Y\) can be easily tested for isomorphism to \(X\) by an extremly 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.

Keywords

Extremal problems in graph theory, linear time, isomorphism testing, canonical labeling, degree sequence of a graph, Parallel algorithms in computer science, random graph

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
173
Top 1%
Top 1%
Top 10%
bronze