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110views more  SIAMDM 2010»
11 years 7 days ago
Embedding Spanning Trees in Random Graphs
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...
Michael Krivelevich
80views Education» more  CORR 2010»
11 years 14 days ago
Distributed Deterministic Edge Coloring using Bounded Neighborhood Independence
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...
Leonid Barenboim, Michael Elkin
11 years 2 months ago
A randomized embedding algorithm for trees
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 ...
Benny Sudakov, Jan Vondrák
138views more  SIAMDM 2010»
11 years 3 months ago
The Last Fraction of a Fractional Conjecture
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...
Frantisek Kardos, Daniel Král', Jean-S&eacu...
101views more  JCT 2010»
11 years 3 months ago
Asymptotically optimal frugal colouring
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...
Michael Molloy, Bruce A. Reed
73views Education» more  CORR 2010»
11 years 4 months ago
Spectrally degenerate graphs: Hereditary case
It is well known that the spectral radius of a tree whose maximum degree is ∆ cannot exceed 2 √
Zdenek Dvorak, Bojan Mohar
82views more  ORL 2007»
11 years 5 months ago
The path partition problem and related problems in bipartite graphs
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...
Jérôme Monnot, Sophie Toulouse
95views more  COMBINATORICS 1999»
11 years 5 months ago
Maximum Degree Growth of the Iterated Line Graph
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
Stephen G. Hartke, Aparna W. Higgins
77views more  COMBINATORICA 1998»
11 years 5 months ago
A Bound on the Total Chromatic Number
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...
Michael Molloy, Bruce A. Reed
84views more  DM 2002»
11 years 5 months ago
On incidence coloring for some cubic graphs
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 ...
Wai Chee Shiu, Peter Che Bor Lam, Dong-Ling Chen