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SIAMDM

2010

11 years 7 days 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

11 years 14 days 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

11 years 2 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

11 years 3 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

11 years 3 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

11 years 4 months ago
2010

Springer

It is well known that the spectral radius of a tree whose maximum degree is ∆ cannot exceed 2 √

ORL

2007

11 years 5 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

11 years 5 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

11 years 5 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

11 years 5 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 ...