Finding Δ(Σ) for a surface σ of characteristic χ(Σ) = −5
Rong Luo, Yue Zhao · Journal of Graph Theory · 2010
For each surface Σ, we define Δ(Σ) = max{Δ(G)|Gis 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