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

Access to Document

10.1016/S0304-0208(08)72838-X

Cite this

@article{be0067f0ab234da4a33541e23880a6e9,

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",

year = "1984",

month = jan,

day = "1",

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

language = "English",

volume = "87",

pages = "307--310",

journal = "North-Holland Mathematics Studies",

issn = "0304-0208",

publisher = "Elsevier",

number = "C",

}

TY - JOUR

T1 - Extending Kotzig's Theorem

T2 - Hensley's Lattice Polytope Theorem

AU - Zaks, Joseph

PY - 1984/1/1

Y1 - 1984/1/1

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 - http://www.scopus.com/inward/record.url?scp=77956934250&partnerID=8YFLogxK

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

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

M3 - Article

AN - SCOPUS:77956934250

SN - 0304-0208

VL - 87

SP - 307

EP - 310

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

Access to Document

Other files and links

Fingerprint

Cite this