Adding random edges to create the square of a Hamilton cycle

Alan Frieze; Andrzej Dudek; Patrick Bennett

Adding random edges to create the square of a Hamilton cycle

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arxiv 1710.02716 v1 pith:TGUSEI2H submitted 2017-10-07 math.CO

Patrick Bennett , Andrzej Dudek , Alan Frieze This is my paper · ORCID

classification math.CO

keywords cycleedgeshamiltonorderrandomsquareaddedadding

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abstract

We consider how many random edges need to be added to a graph of order $n$ with minimum degree $\alpha n$ in order that it contains the square of a Hamilton cycle w.h.p..

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Colour-biased Hamilton cycles in randomly perturbed graphs
math.CO 2025-06 reject novelty 7.0 of 10

Randomly perturbing a graph with O(n) random edges forces a colour-biased Hamilton cycle, and at the critical minimum degree the bias is proportional to m.

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