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On The Attainability Of Upper Bounds For The Circular Chromatic Number Of K4-Minor-Free Graphs., Tracy Lance Holt

Electronic Theses and Dissertations

Let G be a graph. For k ≥ d ≥ 1, a k/d -coloring of G is a coloring c of vertices of G with colors 0, 1, 2, . . ., k - 1, such that d ≤ | c(x) - c(y) | ≤ k - d, whenever xy is an edge of G. We say that the circular chromatic number of G, denoted χ_c(G), is equal to the smallest k/d where a k/d -coloring exists. In [6], Pan and …