Finding Δ(Σ) for a surface σ of characteristic χ(Σ) = −5 | Zendy

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Finding Δ(Σ) for a surface σ of characteristic χ(Σ) = −5

Author(s) -

Luo Rong,

Zhao Yue

Publication year - 2011

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.20548

Subject(s) - planar graph , mathematics , combinatorics , conjecture , graph , surface (topology) , plane (geometry) , outerplanar graph , class (philosophy) , planar , discrete mathematics , line graph , voltage graph , geometry , computer science , artificial intelligence , computer graphics (images)

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

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