Improper colouring of (random) unit disk graphs

نویسندگان

Ross J. Kang

Tobias Müller

Jean-Sébastien Sereni

چکیده

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 only proper colouring).

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Improper 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 کامل

A tight bound for online colouring of disk graphs

We present an improved upper bound on the competitiveness of the online colouring algorithm First-Fit in disk graphs, which are graphs representing overlaps of disks on the plane. We also show that this bound is best possible for deterministic online colouring algorithms that do not use the disk representation of the input graph. We also present a related new lower bound for unit disk graphs. c...

متن کامل

The t-Improper Chromatic Number of Random Graphs

We consider the t-improper chromatic number of the Erdős-Rényi random graph Gn,p. The t-improper chromatic number χ(G) of G is the smallest number of colours needed in a colouring of the vertices in which each colour class induces a subgraph of maximum degree at most t. If t = 0, then this is the usual notion of proper colouring. When the edge probability p is constant, we provide a detailed de...

متن کامل

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 کامل