Extending Kotzig's Theorem: Hensley's Lattice Polytope Theorem

Joseph Zaks

doi:10.1016/S0304-0208(08)72838-X

Extending Kotzig's Theorem: Hensley's Lattice Polytope Theorem

Joseph Zaks

Department of Mathematics

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

Abstract

The weight w(E) of an edge E in a graph G is defined as the sum of the valences of the end-points of E. The weight w(G) of the graph G is defined by w(G) =min{w(E)çEç G}. Kotzig proved that w(G) ≤ 13 holds for all planar graphs, and Grünbaum and Shephard proved that w(G) ≤ 15 holds for all toroidal graphs.

Original language	English
Pages (from-to)	307-310
Number of pages	4
Journal	North-Holland Mathematics Studies
Volume	87
Issue number	C
DOIs	https://doi.org/10.1016/S0304-0208(08)72838-X
State	Published - 1 Jan 1984

ASJC Scopus subject areas

General Mathematics

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title = "Extending Kotzig's Theorem: Hensley's Lattice Polytope Theorem",

abstract = "The weight w(E) of an edge E in a graph G is defined as the sum of the valences of the end-points of E. The weight w(G) of the graph G is defined by w(G) =min\{w(E){\c c}E{\c c} G\}. Kotzig proved that w(G) ≤ 13 holds for all planar graphs, and Gr{\"u}nbaum and Shephard proved that w(G) ≤ 15 holds for all toroidal graphs.",

author = "Joseph Zaks",

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doi = "10.1016/S0304-0208(08)72838-X",

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N2 - The weight w(E) of an edge E in a graph G is defined as the sum of the valences of the end-points of E. The weight w(G) of the graph G is defined by w(G) =min{w(E)çEç G}. Kotzig proved that w(G) ≤ 13 holds for all planar graphs, and Grünbaum and Shephard proved that w(G) ≤ 15 holds for all toroidal graphs.

AB - The weight w(E) of an edge E in a graph G is defined as the sum of the valences of the end-points of E. The weight w(G) of the graph G is defined by w(G) =min{w(E)çEç G}. Kotzig proved that w(G) ≤ 13 holds for all planar graphs, and Grünbaum and Shephard proved that w(G) ≤ 15 holds for all toroidal graphs.

UR - https://www.scopus.com/pages/publications/77956934250

U2 - 10.1016/S0304-0208(08)72838-X

DO - 10.1016/S0304-0208(08)72838-X

M3 - Article

AN - SCOPUS:77956934250

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SP - 307

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JO - North-Holland Mathematics Studies

JF - North-Holland Mathematics Studies

IS - C

ER -

Extending Kotzig's Theorem: Hensley's Lattice Polytope Theorem

Abstract

ASJC Scopus subject areas

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