Upper Embeddability, Girth and the Degree-Sum of Nonadjacent Vertices

Let G be a 2-edge-connected simple graph with girth g , independence number α( G ), and if one of the following two conditions holds α( G ) ≤ 2; α( G ) ≥ 3, and for any three nonadjacent vertices v i  ( i  = 1,2,3), it has , then G is upper embeddable and the lower bound v  − 3 g  + 7 is best possib...

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Bibliographic Details
Published inGraphs and combinatorics Vol. 25; no. 2; pp. 253 - 264
Main Authors Zhangdong, Ouyang, Jing, Wang, Yuanqiu, Huang
Format Journal Article
LanguageEnglish
Published Japan Springer Japan 01.05.2009
Springer Nature B.V
Subjects
Combinatorics
Engineering Design
Mathematics
Mathematics and Statistics
Graph
Maximum genus
Girth
Independence number
Upper embeddability
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Summary:Let G be a 2-edge-connected simple graph with girth g , independence number α( G ), and if one of the following two conditions holds α( G ) ≤ 2; α( G ) ≥ 3, and for any three nonadjacent vertices v i  ( i  = 1,2,3), it has , then G is upper embeddable and the lower bound v  − 3 g  + 7 is best possible. Similarly the result for 3-edge-connected simple graph with girth g and independence number α( G ) is also obtained.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-008-0837-1