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» The independence number in graphs of maximum degree three
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DM
2008
88views more  DM 2008»
14 years 9 months ago
Lower bounding the boundary of a graph in terms of its maximum or minimum degree
A vertex v of a graph G is a boundary vertex if there exists a vertex u such that the distance in G from u to v is at least the distance from u to any neighbour of v. We give the ...
Tobias Müller, Attila Pór, Jean-S&eacu...
DM
2010
143views more  DM 2010»
14 years 9 months ago
Acyclic improper colourings of graphs with bounded maximum degree
For graphs of bounded maximum degree, we consider acyclic t-improper colourings, that is, colourings in which each bipartite subgraph consisting of the edges between two colour cl...
Louigi Addario-Berry, Louis Esperet, Ross J. Kang,...
COMBINATORICA
1998
77views more  COMBINATORICA 1998»
14 years 9 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
JGT
2007
99views more  JGT 2007»
14 years 9 months ago
The upper bound of the number of cycles in a 2-factor of a line graph
Let G be a simple graph with order n and minimum degree at least two. In this paper, we prove that if every odd branch-bond in G has an edge-branch, then its line graph has a 2-fa...
Jun Fujisawa, Liming Xiong, Kiyoshi Yoshimoto, She...
GD
1998
Springer
15 years 1 months ago
An Algorithm for Three-Dimensional Orthogonal Graph Drawing
Abstract. In this paper we present an algorithm for 3-dimensional orthogonal graph drawing based on the movement of vertices from an initial layout along the main diagonal of a cub...
David R. Wood