#### Title

Finding the exact bound of the maximum degrees of class two graphs embeddable in a surface of characteristic is an element of is an element of{-1,-2,-3}

#### Abbreviated Journal Title

J. Comb. Theory Ser. B

#### Keywords

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

#### Abstract

In this paper, we consider the problem of determining the maximum of the set of maximum degrees of class two graphs that can be embedded in a surface. For each surface Sigma, we define Delta(Sigma) = max{Delta(G)vertical bar G is a class two graph of maximum degree Delta that can be embedded in Sigma}. Hence Vizing's Planar Graph Conjecture can be restated as Delta(Sigma) = 5 if Sigma is a plane. We show that Delta(Sigma) = 7 if is an element of(Z) = -1 and Delta(Sigma) = 8 if is an element of(Sigma) is an element of {-2, -3). (c) 2007 Elsevier Inc. All rights reserved.

#### Journal Title

Journal of Combinatorial Theory Series B

#### Volume

98

#### Issue/Number

4

#### Publication Date

1-1-2008

#### Document Type

Article

#### Language

English

#### First Page

707

#### Last Page

720

#### WOS Identifier

#### ISSN

0095-8956

#### Recommended Citation

"Finding the exact bound of the maximum degrees of class two graphs embeddable in a surface of characteristic is an element of is an element of{-1,-2,-3}" (2008). *Faculty Bibliography 2000s*. 662.

http://stars.library.ucf.edu/facultybib2000/662

## Comments

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