Non-Hamiltonian non-Grinbergian graphs

Joseph Zaks

doi:10.1016/0012-365X(77)90165-0

Non-Hamiltonian non-Grinbergian graphs

Joseph Zaks

Department of Mathematics

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

Abstract

Settling a question of Tutte and a similar question of Grünbaum and Zaks, we present a 3-valent 3-connected planar graph that has only pentagons and octagons, has 92 (200, respectively) vertices and its longest circuit (path, respectively) contains at most 90 (198, respectively) vertices; moreover, it is shown that the family of all 3-valent 3-connected planar graphs, having n-gons only if n≡ 2 (mod3) (or n≡ 1 (mod3)), has a shortness exponent which is less than one.

Original language	English
Pages (from-to)	317-321
Number of pages	5
Journal	Discrete Mathematics
Volume	17
Issue number	3
DOIs	https://doi.org/10.1016/0012-365X(77)90165-0
State	Published - 1977

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(77)90165-0

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abstract = "Settling a question of Tutte and a similar question of Gr{\"u}nbaum and Zaks, we present a 3-valent 3-connected planar graph that has only pentagons and octagons, has 92 (200, respectively) vertices and its longest circuit (path, respectively) contains at most 90 (198, respectively) vertices; moreover, it is shown that the family of all 3-valent 3-connected planar graphs, having n-gons only if n≡ 2 (mod3) (or n≡ 1 (mod3)), has a shortness exponent which is less than one.",

author = "Joseph Zaks",

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AB - Settling a question of Tutte and a similar question of Grünbaum and Zaks, we present a 3-valent 3-connected planar graph that has only pentagons and octagons, has 92 (200, respectively) vertices and its longest circuit (path, respectively) contains at most 90 (198, respectively) vertices; moreover, it is shown that the family of all 3-valent 3-connected planar graphs, having n-gons only if n≡ 2 (mod3) (or n≡ 1 (mod3)), has a shortness exponent which is less than one.

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DO - 10.1016/0012-365X(77)90165-0

M3 - Article

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VL - 17

SP - 317

EP - 321

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 3

ER -

Non-Hamiltonian non-Grinbergian graphs

Abstract

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