Non-Hamiltonian simple 3-polytopes whose faces are all 5-gons or 7-gons

✍ Scribed by P.J. Owens

• Publisher: Elsevier Science
• Year: 1981
• Tongue: English
• Weight: 170 KB
• Volume: 36
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/s0012-365x(81)80017-9

✦ Synopsis

Let G3(p, q) denote the class of all simple 3-polytopes (or, equivalently, 3-connected 3-valent planar graphs) with only two types of face, p-gons and q-gons. For any graph G, let u(G) denote the number of vertices and h(G) the length of a maximum cycle. Non-Hamiltonian members of G3(5, q) are known for all q 2 8. Apart from the case q = 10 (see [3]) these graphs are due to J. Zaks (see [5,6,7]).

We prove two theorems concerning the case q = 7.