
doi: 10.1137/0209047
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.
Extremal problems in graph theory, linear time, isomorphism testing, canonical labeling, degree sequence of a graph, Parallel algorithms in computer science, random graph
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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