A fast algorithm on average for solving the Hamilton Cycle problem

Michael Anastos

A fast algorithm on average for solving the Hamilton Cycle problem

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arxiv 2111.14771 v3 pith:XCJWLM4K submitted 2021-11-29 math.CO cs.DS

Michael Anastos This is my paper · ORCID

classification math.COcs.DS

keywords cyclealgorithmcertifyhamhamiltonalonaverageeitherexists

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We present CertifyHAM, an algorithm which takes as input a graph G and either finds a Hamilton cycle of G or it outputs that such a cycle does not exists. If G=G(n, p) and p >2000/n then the expected running time of CertifyHAM is O(n/p). This improves upon previous results due to Gurevich and Shelah, Thomason and Alon and Krivelevich.

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Graph k-Coloring in Average Sublinear Time
cs.DS 2026-07 conditional novelty 8.0 of 10

The exact average-case complexity of k-coloring random k-colorable graphs is Θ(nk) for every k ≤ n^{1/37}.

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