منابع مشابه
Unit Hypercube Visibility Numbers of Trees
A visibility representation of a graph G is an assignment of the vertices of G to geometric objects such that vertices are adjacent if and only if their corresponding objects are “visible” each other, that is, there is an uninterrupted channel, usually axis-aligned, between them. Depending on the objects and definition of visibility used, not all graphs are visibility graphs. In such situations...
متن کاملThe Ramsey numbers of large trees versus wheels
For two given graphs G1 and G2, the Ramseynumber R(G1,G2) is the smallest integer n such that for anygraph G of order n, either $G$ contains G1 or the complementof G contains G2. Let Tn denote a tree of order n andWm a wheel of order m+1. To the best of our knowledge, only R(Tn,Wm) with small wheels are known.In this paper, we show that R(Tn,Wm)=3n-2 for odd m with n>756m^{10}.
متن کاملNew Bounds for Hypercube Slicing Numbers
What is the maximum number of edges of the d-dimensional hypercube, denoted by S d k , that can be sliced by k hyperplanes? This question on combinatorial properties of Euclidean geometry arising from linear separability considerations in the theory of Perceptrons has become an issue on its own. We use computational and combinatorial methods to obtain new bounds for S d k , d 8. These strengthe...
متن کاملSeparation numbers of trees
Let G be a graph on n vertices. Given a bijection f : V (G) → {1, 2, . . . , n}, let |f | = min{|f (u) − f (v)| : uv ∈ E(G)}. The separation number s(G) (also known as antibandwidth [T. Calamoneri, A. Massini, L. Török, I. Vrt’o, Antibandwidth of Complete kary trees, Electronic Notes in Discrete Mathematics 24 (2006), 259–266; A. Raspaud, H. Schroder, O. Sykora, L. Török, I. Vrt’o, Antibandwidt...
متن کاملEmbedding complete trees into the hypercube
We consider embeddings of the complete t-ary trees of depth k (denotation T k,t) as subgraphs into the hypercube of minimum dimension n. This n, denoted by dim(T k,t), is known if max{k, t} ≤ 2. First we study the next open case max{k, t} = 3. We improve the known upper bound dim(T k,3) ≤ 2k + 1 up to limk→∞ dim(T k,3)/k ≤ 5/3 and derive the asymptotic limt→∞ dim(T 3,t)/t = 227/120. As a co-res...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2017
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-017-1779-2