## On the k-orientability of random graphs (2009)

by
Luc Devroye
,
Ebrahim Malalla

Citations: | 1 - 0 self |

### BibTeX

@MISC{Devroye09onthe,

author = {Luc Devroye and Ebrahim Malalla},

title = { On the k-orientability of random graphs},

year = {2009}

}

### OpenURL

### Abstract

Let G(n, m) be an undirected random graph with n vertices and m multiedges that may include loops, where each edge is realized by choosing its two vertices independently and uniformly at random with replacement from the set of all n vertices. The random graph G(n, m) is said to be k-orientable, where k ≥ 2 is an integer, if there exists an orientation of the edges such that the maximum out-degree is at most k. Let ck = sup {c: G(n, cn) is k-orientable w.h.p.}. We prove that for k large enough, 1 − 2 k exp −k + 1 + e −k/4) < ck/k < 1 − exp