Planar unit-distance graphs having planar unit-distance complement
نویسندگان
چکیده
منابع مشابه
A lower bound for 4-regular planar unit distance graphs
We perform an exhaustive search for the minimum 4-regular unit distance graph resulting in a lower bound of 34 vertices.
متن کاملOn -unit distance graphs
We consider a variation on the problem of determining the chromatic number of the Euclidean plane and define the -unit distance graph to be the graph whose vertices are the points of E, in which two points are adjacent whenever their distance is within of 1. For certain values of we are able to show that the chromatic number is exactly seven. For some smaller values we show the chromatic number...
متن کاملImproved Distance Queries in Planar Graphs
There are several known data structures that answer distance queries between two arbitrary vertices in a planar graph. The tradeoff is among preprocessing time, storage space and query time. In this paper we present three data structures that answer such queries, each with its own advantage over previous data structures. The first one improves the query time of data structures of linear space. ...
متن کاملPlanar 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...
متن کاملExact distance oracles for planar graphs
We present new and improved data structures that answer exact node-to-node distance queries in planar graphs. Such data structures are also known as distance oracles. For any directed planar graph on n nodes with non-negative lengths we obtain the following: • Given a desired space allocation S ∈ [n lg lgn, n], we show how to construct in Õ(S) time a data structure of size O(S) that answers dis...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.04.050