Bruce A. Reed

Learn More
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 such graphs almost surely have a giant component, while if P i(i?2) i < 0 then almost surely all components in such graphs are small. We can apply these results(More)
Given a sequence of non-negative real numbers 0 ; 1 ; : : : which sum to 1, we consider a random graph having approximately i n ver-tices of degree i. In 12] the authors essentially show that if P i(i ? 2) i > 0 then the graph a.s. has a giant component, while if P i(i ? 2) i < 0 then a.s. all components in the graph are small. In this paper we analyze the(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 triangular lattice in the plane. We investigated the corresponding weighted coloring problem of assigning sets of colors to vertices of the triangular lattice so that(More)
A vertex coloring of a graph G is called acyclic if no two adjacent vertices have the same color and there is no two-colored cycle in G. The acyclic chromatic number of G , denoted by A ( G ) , is the least number of colors in an acyclic coloring of G. We show that if G has maximum degree d, then A ( G ) = O(d413) as d+m. This settles a problem of Erdos who(More)