论文信息 - Non-Hamiltonian simple 3-polytopes having just two types of faces

Non-Hamiltonian simple 3-polytopes having just two types of faces

It is shown that for every value of an integer k, k>=11, there exist 3-valent 3-connected planar graphs having just two types of faces, pentagons and k-gons, and which are non- Hamiltonian. Moreover, there exist @[email protected](k) > 0, for these values of k, and sequences (G"n)^~"n"="1 of the said graphs for which V(G"n)->~ and the size of a largest circuit of G"n is at most ([email protected])V(G"n); similar result for the size of a largest path in such graphs is established for all k, k>=11, except possibly for k = 14, 17, 22 and k = 5m+ 5 for all m>=2.

Joseph Zaks

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