## Abstract The generalized Petersen graph __P__(6__k__ + 3, 2) has exactly 3 Hamiltonian cycles for __k__ ≥ 0, but for __k__ ≥ 2 is not uniquely edge colorable. This disproves a conjecture of Greenwell and Kronk [1].
Three small cubic graphs with interesting hamiltonian properties
✍ Scribed by Tudor Zamfirescu
- Publisher
- John Wiley and Sons
- Year
- 1980
- Tongue
- English
- Weight
- 211 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0364-9024
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✦ Synopsis
Abstract
We present here three graphs, which are the smallest known ones of their kind: a cubic three‐connected planar nontraceable graph, a cubic three‐connected planar graph which is not homogeneously traceable, and a cubic one‐Hamiltonian graph which is not Hamiltonian connected.
📜 SIMILAR VOLUMES
We consider the maximum number of vertices in a cubic graph with small diameter. We show that a cubic graph of diameter 4 has at most 40 vertices. (The Moore bound is 46 and graphs with 38 vertices are known.) We also consider bipartite cubic graphs of diameter 5, for which the Moore bound is 62. We
Bauer, D., G. Fan and H.J. Veldman, Hamiltonian properties of graphs with large neighborhood unions, Discrete Mathematics 96 (1991) 33-49. Let G be a graph of order n, a k =min{~ki=ld(vi): {V 1 ..... Vn} is an independent set of vertices in G}, NC=min{IN(u) 13N(v)l:uv~E(G)} and NC2=min{IN(u) t3 wh