Finding Δ (Σ) For A Surface Σ Of Characteristic - 6 And - 7

Keywords

Class one; Class two; Critical graphs; Edge colorings; Surfaces

Abstract

For each surface Σ , we define Δ (Σ) = max{Δ(G)|G is a class two graph with 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 sphere. For a surface Σ , if χ(Σ) ∈ { - 5 , - 4 , ⋯ , 0 } , Δ (Σ) is already known. In this paper, we show that Δ (Σ) = 10 if Σ is a surface of characteristic χ(Σ) ∈ { - 6 , - 7 }.

Publication Date

7-1-2017

Publication Title

Graphs and Combinatorics

Volume

33

Issue

4

Number of Pages

929-944

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00373-017-1780-9

Socpus ID

85020289776 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85020289776

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