#### Title

Finding Delta(Sigma) for a Surface Sigma of Characteristic chi(Sigma) =-5

#### Abbreviated Journal Title

J. Graph Theory

#### Keywords

edge colorings; class one; class two; critical graphs; surfaces; INDEX-CRITICAL GRAPHS; EDGE COLORINGS; MAXIMUM DEGREE-7; Mathematics

#### Abstract

For each surface Sigma, we define Delta(Sigma)= max{Delta(G)|G is a class two graph of maximum degree Delta(G) that can be embedded in Sigma}. Hence, Vizing's Planar Graph Conjecture can be restated as Delta(Sigma) = 5 if Sigma is a plane. In this paper, we show that Delta(Sigma)= 9 if Sigma is a surface of characteristic chi(Sigma) = -5. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 68: 148-168, 2011

#### Journal Title

Journal of Graph Theory

#### Volume

68

#### Issue/Number

2

#### Publication Date

1-1-2011

#### Document Type

Article

#### DOI Link

#### Language

English

#### First Page

148

#### Last Page

168

#### WOS Identifier

#### ISSN

0364-9024

#### Recommended Citation

"Finding Delta(Sigma) for a Surface Sigma of Characteristic chi(Sigma) =-5" (2011). *Faculty Bibliography 2010s*. 1602.

http://stars.library.ucf.edu/facultybib2010/1602

## Comments

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