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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.CO2008
On the chromatic number of random d-regular graphs
Graeme Kemkes, Xavier Pérez-Giménez, Nicholas Wormald
In this work we show that, for any fixed d, random d-regular graphs asymptotically almost surely can be coloured with k colours, where k is the smallest integer satisfying d<2(k-1)…