Three distance theorem and grid graph
نویسنده
چکیده
We will prove a d-dimensional version of the Geelen and Simpson theorem. c © 2000 Elsevier Science B.V. All rights reserved.
منابع مشابه
The Existence Theorem for Contractive Mappings on $wt$-distance in $b$-metric Spaces Endowed with a Graph and its Application
In this paper, we study the existence and uniqueness of fixed points for mappings with respect to a $wt$-distance in $b$-metric spaces endowed with a graph. Our results are significant, since we replace the condition of continuity of mapping with the condition of orbitally $G$-continuity of mapping and we consider $b$-metric spaces with graph instead of $b$-metric spaces, under which can be gen...
متن کاملLine completion number of grid graph Pn × Pm
The concept of super line graph was introduced in the year 1995 by Bagga, Beineke and Varma. Given a graph with at least r edges, the super line graph of index r, Lr(G), has as its vertices the sets of r-edges of G, with two adjacent if there is an edge in one set adjacent to an edge in the other set. The line completion number lc(G) of a graph G is the least positive integer r for which Lr(G) ...
متن کاملGeometric Separators and Their Applications to Protein Folding in the HP-Model
We develop a new method for deriving a geometric separator for a set of grid points. Our separator has a linear structure, which can effectively partition a grid graph. For example, we prove that for a grid graph G with a set of n points P in a two-dimensional grid, there is a separator with at most 1.129 √ n points in P that partitions G into two disconnected grid graphs each with at most 2n 3...
متن کاملA Note on Erdős-diophantine Graphs and Diophantine Carpets
A Diophantine figure, see i.e. [4, 5, 6], is a set of points on the integer grid Z where all mutual Euclidean distances are integers. We also speak of Diophantine graphs. The vertices are points in Z (the coordinates) and the edges are labeled with the distance between the two adjacent vertices, which is integral. In this language a Diophantine figure is a complete Diophantine graph. Two Diopha...
متن کاملSmith’s Theorem and a characterization of the 6-cube as distance-transitive graph
A generic distance-regular graph is primitive of diameter at least two and valency at least three. We give a version of Derek Smith’s famous theorem for reducing the classification of distance-regular graphs to that of primitive graphs. There are twelve cases—the generic case, four canonical imprimitive cases that reduce to the generic case, and seven exceptional cases. All distance-transitive ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 223 شماره
صفحات -
تاریخ انتشار 2000