graphs is at most log, 6.
On the shortness exponent of 1-tough, maximal planar graphs
✍ Scribed by Michal Tkáč
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 454 KB
- Volume
- 154
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
It is shown that the shortness exponent of the class of l-tough, maximal planar graphs is at most log, 5. The non-Hamiltonian, l-tough, maximal planar graph with a minimum number of vertices is presented.
📜 SIMILAR VOLUMES
## Abstract We consider the problem of the minimum number of Hamiltonian cycles that could be present in a Hamiltonian maximal planar graph on __p__ vertices. In particular, we construct a __p__‐vertex maximal planar graph containing exactly four Hamiltonian cycles for every __p__ ≥ 12. We also pro
## Abstract Let __p__ and __C__~4~ (__G__) be the number of vertices and the number of 4‐cycles of a maximal planar graph __G__, respectively. Hakimi and Schmeichel characterized those graphs __G__ for which __C__~4~ (__G__) = 1/2(__p__^2^ + 3__p__ ‐ 22). This characterization is correct if __p__ ≥
Let G be a maximal planar graph with p vertices, and let Ck(G) denote the number of cycles of length k in G. We first present tight bounds for C,(G) and C,(G) in terms of p. We then give bounds for Ck(G) when 5 5 k 5 p , and consider in particular bounds for C,(G), in terms of p. Some conjectures an
## Abstract A Hamiltonian walk of a connected graph is a shortest closed walk that passes through every vertex at least once, and the length of a Hamiltonian walk is the total number of edges traversed by the walk. We show that every maximal planar graph with __p__(≥ 3) vertices has a Hamiltonian c