Local 7-coloring for planar subgraphs of unit disk graphs

Local 7-Coloring for Planar Subgraphs of Unit Disk Graphs

The problem of computing locally a coloring of an arbitrary planar subgraph of a unit disk graph is studied. Each vertex knows its coordinates in the plane, can directly communicate with all its neighbors within unit distance. Using this setting, first a simple algorithm is given whereby each vertex can compute its color in a 9-coloring of the planar graph using only information on the subgraph...

Improper coloring of unit disk graphs

Planar Hop Spanners for Unit Disk Graphs

The simplest model of a wireless network graph is the Unit Disk Graph (UDG): an edge exists in UDG if the Euclidean distance between its endpoints is ≤ 1. The problem of constructing planar spanners of Unit Disk Graphs with respect to the Euclidean distance has received considerable attention from researchers in computational geometry and ad-hoc wireless networks. In this paper, we present an a...

Acyclic list 7-coloring of planar graphs

Theacyclic list chromatic numberof every planar graph is proved to be at most 7. 2002 Wiley Periodicals, Inc. J Graph Theory 40: 83–90, 2002

Local 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....