## Abstract Let __G__ be a graph of order __n__ with exactly one Hamiltonian cycle and suppose that __G__ is maximal with respect to this property. We determine the minimum number of edges __G__ can have.
A census of maximum uniquely hamiltonian graphs
β Scribed by Curtiss A. Barefoot; R. C. Entringer
- Publisher
- John Wiley and Sons
- Year
- 1981
- Tongue
- English
- Weight
- 261 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
We show that there are 2^[n/2]β4^ largest graphs of order n β₯ 7 having exactly one hamiltonian cycle. a recursive procedure for constructing these graphs is described.
π SIMILAR VOLUMES
Let G be a uniquely hamiltonian graph on n vertices. We show that G has a vertex of degree at most c log 2 8n+3, where c=(2&log 2 3) &1 r2.41. We show further that G has at least two vertices of degree less than four if it is planar and at least four vertices of degree two if it is bipartite.
## Abstract A (1,2)βeulerian weight __w__ of a grph is hamiltonian if every faithful cover of __w__ is a set of two Hamilton circuits. Let __G__ be a 3βconnected cubic graph containing no subdivition of the Petersen graph. We prove that if __G__ admits a hamiltonian weight then __G__ is uniquely 3β
The hamiltonian path graph H(F) of a graph F is that graph having the same vertex set as F and in which two vertices u and u are adjacent if and only if F contains a hamiltonian u -u path. First, in response to a conjecture of Chartrand, Kapoor and Nordhaus, a characterization of nonhamiltonian grap
## Abstract In this paper, we show that __n__ β©Ύ 4 and if __G__ is a 2βconnected graph with 2__n__ or 2__n__β1 vertices which is regular of degree __n__β2, then __G__ is Hamiltonian if and only if __G__ is not the Petersen graph.
## Abstract We construct 3βregular (cubic) graphs __G__ that have a dominating cycle __C__ such that no other cycle __C__~1~ of __G__ satisfies __V(C)__ β __V__(__C__~1~). By a similar construction we obtain loopless 4βregular graphs having precisely one hamiltonian cycle. The basis for these const