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Full-Text Articles in Discrete Mathematics and Combinatorics
Edge Colorings Of Graphs On Surfaces And Star Edge Colorings Of Sparse Graphs, Katherine M. Horacek
Edge Colorings Of Graphs On Surfaces And Star Edge Colorings Of Sparse Graphs, Katherine M. Horacek
Graduate Theses, Dissertations, and Problem Reports
In my dissertation, I present results on two types of edge coloring problems for graphs.
For each surface Σ, we define ∆(Σ) = max{∆(G)| G is a class two graph with maximum degree ∆(G) that can be embedded in Σ}. Hence Vizing’s Planar Graph Conjecture can be restated as ∆(Σ) = 5 if Σ is a sphere. For a surface Σ with characteristic χ(Σ) ≤ 0, it is known ∆(Σ) ≥ H(χ(Σ))−1, where H(χ(Σ)) is the Heawood number of the surface, and if the Euler char- acteristic χ(Σ) ∈ {−7, −6, . . . , −1, 0}, ∆(Σ) is already …