Given a sequence of non-negative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n ver-tices of degree i. Essentially, we show that if P i(i?2) i > 0 thenâ€¦ (More)

Given a sequence of non negative real numbers which sum to we consider a random graph having approximately in ver tices of degree i In the authors essentially show that if P i i i then the graph a sâ€¦ (More)

Coloring is an abstraction for partitioning a set of objects into a few independent sets. The notion of independence and the associated coloring rules vary from context to context. In the simplestâ€¦ (More)

We provide a met.hod to produce an efficient algorithm to find an object whose existence is guaranteed by the Lo&z Local Lemma. We feel that this method will apply to the vast. majority ofâ€¦ (More)

In cellular telephone networks, sets of radio channels (colors) must be assigned to transmitters (vertices) while avoiding interference. Often, the transmitters are laid out like vertices of aâ€¦ (More)

We show that for any fixed <italic>k</italic>, there is a linear-time algorithm which given a graph <italic>G</italic> either: (i) finds a cutset <italic>X</italic> of <italic>G</italic> withâ€¦ (More)