## Abstract Let __Q__~__n__~ denote the nβdimensional hypercube. In this paper we derive upper and lower bounds for the crossing number __v__(__Q__~__n__~), i.e., the minimum number of edgeβcrossings in any planar drawing of __Q__~__n__~. The upper bound is close to a result conjectured by Eggleton
Bounds on the number of Hamiltonian circuits in the n-cube
β Scribed by Robert James Douglas
- Publisher
- Elsevier Science
- Year
- 1977
- Tongue
- English
- Weight
- 224 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
New upper anti lower ~,ounds arc found for the number of HamilI(,nian circuits in the graph of Ihe r -cube.
(2) -1 i,, ,,'
We show that h(n)~ [n(n -I)/212 .... '~'"""',"' = U~(e,)
(3)
π SIMILAR VOLUMES
It is proved that if a planar triangulation different from K3 and K4 contains a Hamiltonian cycle, then it contains at least four of them. Together with the result of Hakimi, Schmeichel, and Thomassen [21, this yields that, for n 2 12, the minimum number of Hamiltonian cycles in a Hamiltonian planar
The main results assert that the minimum number of Hamiltonian bypasses in a strong tournament of order n and the minimum number of Hamiltonian cycles in a 2-connected tournament of order n increase exponentially with n. Furthermore, the number of Hamiltonian cycles in a tournament increases at leas
A cube-like graph is a graph whose vertices are all 2" subsets of a set E of cardinality n, in which two vertices are adjacent if their symmetric difference is a member of a given specified collection of subsets of E. Many authors were interested in the chromatic number of such graphs and thought it
Fisher, D.C. and J. Ryan, Bounds on the number of complete subgraphs, Discrete Mathematics 103 (1992) 313-320. Let G be a graph with a clique number w. For 1 s s w, let k, be the number of complete j subgraphs on j nodes. We show that k,,, c (j~l)(kj/(~))u""'. This is exact for complete balanced w-