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- Michael Molloy, Bruce A. Reed
- Random Struct. Algorithms
- 1995

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)

- Michael Molloy, Bruce A. Reed
- Combinatorics, Probability & Computing
- 1998

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)

- Vasek Chvátal, Bruce A. Reed
- FOCS
- 1992

- Bruce A. Reed, Kaleigh Smith, Adrian Vetta
- Oper. Res. Lett.
- 2004

- Michael Molloy, Bruce A. Reed
- STOC
- 1998

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 applications of the Local Lemma, unless t,he application has one of four problematic traits. However, proving that the method applies to a particular application may… (More)

- Colin McDiarmid, Bruce A. Reed
- Networks
- 2000

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)

- Bruce A. Reed
- STOC
- 1992

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 |<italic>X</italic>| ≤ <italic>k</italic> such that no component of <italic>G</italic>–<italic>X</italic> contains more than… (More)

- Noga Alon, Colin McDiarmid, Bruce A. Reed
- Random Struct. Algorithms
- 1991

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)

- Bruce A. Reed, Neil Robertson, Paul D. Seymour, Robin Thomas
- Combinatorica
- 1996

We prove a conjecture of Younger, that for every integer n ≥ 0 there exists an integer t ≥ 0 such that for every digraph G, either G has n vertex-disjoint directed circuits, or G can be made acyclic by deleting at most t vertices.

- Michael Molloy, Bruce A. Reed
- J. Comb. Theory, Ser. B
- 1997