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Note on two problems of J. Zaks concerning Hamiltonian 3-polytopes

✍ Scribed by Hansjoachim Walther

Publisher
Elsevier Science
Year
1981
Tongue
English
Weight
313 KB
Volume
33
Category
Article
ISSN
0012-365X

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✦ Synopsis

Let us denote by G(m, n) the family of all simple 3-poiytopes having ,just two types of faces, m-gons and n-gons. J. Z&s [3] proved that G(5; k) contains non-Hamiltonian members for all k, k 3 11, and asked among others the folfowing question: Do there exist non-Hamiltonian members in any of the families G(4; k) and G(3; k) for k 37?

.

We can prove the following ' .

Tborem I. G(4; k) contczim non-Hamhwtian members for akl odd k, k 3 9.

We will prove this theorem here only for k = 9, by constructing an appropriate graph 2 in G(4; 9). In a later paper we will show The~mm 2. The shortness exponent (see [l]) of the family G(4;k) is smaller than 1 for all odd k, k 3 17.

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