Colouring stability two unit disk graphs
نویسنده
چکیده
We prove that every stability two unit disk graph has chromatic number at most 3 2 times its clique number.
منابع مشابه
Improper 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 کاملA 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 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 کاملLocal Edge Colouring of Yao-Like Subgraphs of Unit Disk Graphs
The focus of the present paper is on providing a local deterministic algorithm for colouring the edges of Yao-like subgraphs of Unit Disc Graphs. These are geometric graphs such that for some positive integers l, k the following property holds at each node v: if we partition the unit circle centered at v into 2k equally sized wedges then each wedge can contain at most l points different from v....
متن کاملSome colouring problems for unit-quadrance graphs
The quadrance between two points A1 = (x1, y1) and A2 = (x2, y2) is the number Q(A1, A2) = (x1 − x2) + (y1 − y2). Let q be an odd prime power and Fq be the finite field with q elements. The unit-quadrance graph Dq has the vertex set F 2 q , and X,Y ∈ F 2 q are adjacent if and only if Q(A1, A2) = 1. In this paper, we study some colouring problems for the unit-quadrance graph Dq and discuss some ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Contributions to Discrete Mathematics
دوره 8 شماره
صفحات -
تاریخ انتشار 2013