Non-hamiltonian cubic planar graphs having just two types of faces

Joseph Zaks

doi:10.1016/S0167-5060(08)70067-0

Non-hamiltonian cubic planar graphs having just two types of faces

Joseph Zaks

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This chapter discusses the non-Hamiltonian cubic planar graphs having two types of faces. It is assumed that G(m, n) denote the family of all the cubic, 3-connected planar graphs having just two types of faces, m-gons and n-gons. All the members of G(3, 6) were described by Grünbaum and Motzkin. Goodey proved, in relation to Barnette's Conjecture, that all the members of G(4, 6) are Hamiltonian. All the members of G(m, n) are Hamiltonian. For every k, k ≥ 11, G(5, k) contains non-Hamiltonian members.

Original language	English
Pages (from-to)	225-227
Number of pages	3
Journal	Annals of Discrete Mathematics
Volume	9
Issue number	C
DOIs	https://doi.org/10.1016/S0167-5060(08)70067-0
State	Published - 1 Jan 1980

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1016/S0167-5060(08)70067-0

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abstract = "This chapter discusses the non-Hamiltonian cubic planar graphs having two types of faces. It is assumed that G(m, n) denote the family of all the cubic, 3-connected planar graphs having just two types of faces, m-gons and n-gons. All the members of G(3, 6) were described by Gr{\"u}nbaum and Motzkin. Goodey proved, in relation to Barnette's Conjecture, that all the members of G(4, 6) are Hamiltonian. All the members of G(m, n) are Hamiltonian. For every k, k ≥ 11, G(5, k) contains non-Hamiltonian members.",

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AB - This chapter discusses the non-Hamiltonian cubic planar graphs having two types of faces. It is assumed that G(m, n) denote the family of all the cubic, 3-connected planar graphs having just two types of faces, m-gons and n-gons. All the members of G(3, 6) were described by Grünbaum and Motzkin. Goodey proved, in relation to Barnette's Conjecture, that all the members of G(4, 6) are Hamiltonian. All the members of G(m, n) are Hamiltonian. For every k, k ≥ 11, G(5, k) contains non-Hamiltonian members.

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Non-hamiltonian cubic planar graphs having just two types of faces

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