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math.GM2018
Francis Guthrie's approach to The Four Color Problem
Asbjørn Brændeland
The odd wheel is the only type of 4-critical graph in which one vertex always gets a unique color. This supports Frederic Guthrie's approach to the Four Color Problem.
math.GM2014★ 1 cited
Color fixation and color identity in 4-chromatic graphs
Asbjørn Brændeland
I argue that there is no 4-chromatic planar graph with a joinable pair of color identical vertices, i.e., given a 4-chromatic planar graph G and a pair of vertices {u, v} in G, if…
math.GM2014★ 2 cited
Color identical pairs in 4-chromatic graphs
Asbjørn Brændeland
I argue that, given vertices u and v in a 4-chromatic graph G, if the color of u equals the color of v in every 4-coloring of G then G has no planar supergraph where u and v are ad…