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 then… (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 s… (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 simplest… (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 of… (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 a… (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> with… (More)