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math.CO2009
O-cycles, vertex-oriented graphs, and the four colour theore
Ortho Flint, Stuart Rankin
In 1880, P. G. Tait showed that the four colour theorem is equivalent to the assertion that every 3-regular planar graph without cut-edges is 3-edge-colourable, and in 1891, J. Pet…
math.CO2009
Fine-Wilf graphs and the generalized Fine-Wilf theorem
Stuart A. Rankin
In 1962, R. C. Lyndon and M. P. Shutzenberger established that for any positive integers r and s, any sequence of length at least r+s that is both r-periodic and s-periodic is then…