SIAMDM
2010
12 years 11 months ago
2010
We prove that if T is a tree on n vertices with maximum degree and the edge probability p(n) satisfies: np C max{ log n, n } for some constant > 0, then with high probability...
CORR
2010
Springer
12 years 11 months ago
2010
Springer
We study the edge-coloring problem in the message-passing model of distributed computing. This is one of the most fundamental problems in this area. Currently, the best-known dete...
COMBINATORICA
2010
13 years 1 months ago
2010
In this paper, we propose a simple and natural randomized algorithm to embed a tree T in a given graph G. The algorithm can be viewed as a "self-avoiding tree-indexed random ...
SIAMDM
2010
13 years 2 months ago
2010
Reed conjectured that for every ε > 0 and every integer ∆, there exists g such that the fractional total chromatic number of every graph with maximum degree ∆ and girth at...
JCT
2010
13 years 2 months ago
2010
We prove that every graph with maximum degree ∆ can be properly (∆ + 1)coloured so that no colour appears more than O(log ∆/ log log ∆) times in the neighbourhood of any v...
CORR
2010
Springer
13 years 3 months ago
2010
Springer
It is well known that the spectral radius of a tree whose maximum degree is ∆ cannot exceed 2 √
ORL
2007
13 years 4 months ago
2007
We prove that it is NP-complete to decide whether a bipartite graph of maximum degree three on nk vertices can be partitioned into n paths of length k. Finally, we propose some ap...
COMBINATORICS
1999
13 years 4 months ago
1999
Let k denote the maximum degree of the kth iterated line graph Lk(G). For any connected graph G that is not a path, the inequality k+1 2k - 2 holds. Niepel, Knor, and Solt
COMBINATORICA
1998
13 years 4 months ago
1998
We prove that the total chromatic number of any graph with maximum degree is at most plus an absolute constant. In particular, we show that for su ciently large, the total chromat...
DM
2002
13 years 4 months ago
2002
In 1993, Brualdi and Massey conjectured that every graph can be incidence colored with + 2 colors, where is the maximum degree of a graph. Although this conjecture was solved in ...