3 citations · 3 across the 3 of their papers we have counts for
4 papers
Towards a weighted version of the Hajnal-Szemerédi Theorem
József Balogh, Graeme Kemkes, Choongbum Lee +1
For a positive integer r>=2, a K_r-factor of a graph is a collection vertex-disjoint copies of K_r which covers all the vertices of the given graph. The celebrated theorem of Hajna…
Asymptotic enumeration of sparse 2-connected graphs
Graeme Kemkes, Cristiane M. Sato, Nicholas Wormald
We determine an asymptotic formula for the number of labelled 2-connected (simple) graphs on vertices and edges, provided that and as $n\to\in…
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…
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)…