On the entire coloring conjecture

被引：22

作者：

Sanders, DP ^{[1
]}

Zhao, Y ^{[1
]}

机构：

[1] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2000年 / 43卷 / 01期

关键词：

D O I：

10.4153/CMB-2000-017-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Four Color Theorem says that the faces (or vertices) of a plane graph may be colored with four colors. Vizing's Theorem says that the edges of a graph with maximum degree Delta may be colored with Delta + 1 colors. In 1972, Kronk and Mitchem conjectured that the vertices, edges, and faces of a plane graph may be simultaneously colored with Delta + 4 colors. In this article, we give a simple proof that the conjecture is true if Delta greater than or equal to 6.

引用

页码：108 / 114

页数：7

共 21 条

[1] EVERY PLANAR MAP IS 4 COLORABLE [J].

APPEL, K ;

HAKEN, W .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 82 (05) :711-712

[2]

Borodin O. V., 1984, Metody Diskret. Analiz., V108, P12

[3]

Borodin OV, 1996, J GRAPH THEOR, V23, P233, DOI 10.1002/(SICI)1097-0118(199611)23:3<233::AID-JGT3>3.0.CO

[4]

2-T

[5]

BORODIN OV, 1989, J REINE ANGEW MATH, V394, P180

[6]

FIAMCIK J, 1971, MAT CAS, V21, P9

[7]

JENSEN TR, 1995, GRAPH COLORNG PROBLE, P47

[8]

JUCOVIC E, 1969, MAT CAS, V19, P225

[9]

Kronk H. V., 1973, Discrete Mathematics, V5, P253, DOI 10.1016/0012-365X(73)90142-8

[10] ENTIRE CHROMATIC NUMBER OF A NORMAL GRAPH IS AT MOST 7 [J].

KRONK, HV ;

MITCHEM, J .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 78 (05) :799-&

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