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20052009
most citedAn improved upper bound on the length of the longest cycle of a supercritical random graph

3 citations · 7 across the 10 of their papers we have counts for

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math.CO2009★ 1 cited

Disjoint Hamilton cycles in the random geometric graph

Xavier Pérez-Giménez, Nicholas C. Wormald

We prove a conjecture of Penrose about the standard random geometric graph process, in which n vertices are placed at random on the unit square and edges are sequentially added in…

math.CO2009★ 3 cited

An improved upper bound on the length of the longest cycle of a supercritical random graph

Graeme Kemkes, Nicholas Wormald

We improve Luczak's upper bounds on the length of the longest cycle in the random graph G(n,M) in the "supercritical phase" where M=n/2+s and s=o(n) but n^{2/3}=o(s). The new upper…