Finding Δ(Σ) For A Surface Σ Of Characteristic −4

Keywords

class one; class two; critical graphs; edge colorings; surfaces

Abstract

For each surface Σ, we define (Formula presented.) max (Formula presented.) G is a class two graph of maximum degree (Formula presented.) that can be embedded in (Formula presented.). Hence, Vizing's Planar Graph Conjecture can be restated as (Formula presented.) if Σ is a sphere. In this article, by applying some newly obtained adjacency lemmas, we show that (Formula presented.) if Σ is a surface of characteristic (Formula presented.). Until now, all known (Formula presented.) satisfy (Formula presented.). This is the first case where (Formula presented.).

Publication Date

11-1-2016

Publication Title

Journal of Graph Theory

Volume

83

Issue

3

Number of Pages

277-302

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1002/jgt.21997

Socpus ID

84987792422 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84987792422

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