منابع مشابه
Weighted Improper Colouring
In this paper, we study a colouring problem motivated by a practical frequency assignment problem and up to our best knowledge new. In wireless networks, a node interferes with the other nodes the level of interference depending on numerous parameters: distance between the nodes, geographical topography, obstacles, etc. We model this with a weighted graph G where the weights on the edges repres...
متن کاملImproper colouring of (random) unit disk graphs
For any graph G, the k-improper chromatic number χ(G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree k. We investigate the ratio of the kimproper chromatic number to the clique number for unit disk graphs and random unit disk graphs to extend results of McDiarmid and Reed (1999); McDiarmid (2003) (where they considered...
متن کاملImproper colouring of unit disk graphs
Motivated by a satellite communications problem, we consider a generalised colouringproblem on unit disk graphs. A colouring is k-improper if no vertex receives the same colouras k+1 of its neighbours. The k-improper chromatic number χ(G) the least number of coloursneeded in a k-improper colouring of a graph G. The main subject of this work is analysingthe complexity of computin...
متن کاملAbout a Brooks-type theorem for improper colouring
A graph is k-improperly -colourable if its vertices can be partitioned into parts such that each part induces a subgraph of maximum degree at most k. A result of Lovász states that for any graph G, such a partition exists if ≥ ⌈ Δ(G)+1 k+1 ⌉ . When k = 0, this bound can be reduced by ∗ This work was partially supported by the Égide eco-net project 16305SB. † Partially supported by the Brazilian...
متن کاملBounds and Fixed-Parameter Algorithms for Weighted Improper Coloring
We study the weighted improper coloring problem, a generalization of defective coloring. We present some hardness results and in particular we show that weighted improper coloring is not fixed-parameter tractable when parameterized by pathwidth. We generalize bounds for defective coloring to weighted improper coloring and give a bound for weighted improper coloring in terms of the sum of edge w...
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ژورنال
عنوان ژورنال: Journal of Discrete Algorithms
سال: 2012
ISSN: 1570-8667
DOI: 10.1016/j.jda.2012.07.001