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Shortness exponents of families of graphs

✍ Scribed by Branko Grünbaum; Hansjoachim Walther

Book ID
103504682
Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
961 KB
Volume
14
Category
Article
ISSN
0097-3165

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📜 SIMILAR VOLUMES

Bipartite cubic graphs and a shortness e
Bipartite cubic graphs and a shortness exponent
✍ P.J. Owens 📂 Article 📅 1983 🏛 Elsevier Science 🌐 English ⚖ 148 KB

The class of 3-connected bipartite cubic graphs is shown to contain a oon-Hamiltonian graph with only 78 vertices and to have a shortness exponent less than one. In this paper, a graph is a simple undirected gaph and a subgraph is an induced subgraph. For a~ay graph G, v(G) denotes the number of ve

5-regular 3-polytopal graphs with edges
5-regular 3-polytopal graphs with edges of only two types and shortness exponents less than one
✍ J. Harant; P.J. Owens; M. Tkáč; H. Walther 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 309 KB

It is shown that, if q >/29 and q ~ 0 (mod 3), the infinite class of 5-regular 3-polytopal graphs whose edges are incident with either two triangles or a triangle and a q-gon contains nonhamiltonian members and even has shortness exponent less than one.

On the shortness exponent of 1-tough, ma
On the shortness exponent of 1-tough, maximal planar graphs
✍ Michal Tkáč 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 454 KB

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.

A shortness exponent for r-regular r-con
A shortness exponent for r-regular r-connected graphs
✍ Brad Jackson; T. D. Parsons 📂 Article 📅 1982 🏛 John Wiley and Sons 🌐 English ⚖ 302 KB 👁 1 views

## Abstract Let __r__≧ 3 be an integer. It is shown that there exists ε= ε(__r__), 0 < ε < 1, and an integer __N__ = __N(r__) > 0 such that for all __n__ ≧ __N__ (if __r__ is even) or for all even __n__ ≧ __N__(if __r__ is odd), there is an __r__‐connected regular graph of valency __r__ on exactly