Perfect 1-Factorizations of Graphs
Perfect 1-Factorizations of Graphs
A perfect 1-factorization (P1F) of a -regular graph is a proper edge coloring using colors (meaning: two edges that meet at a vertex get different colors) so that the union of any two colors forms a Hamiltonian cycle. A graph with a P1F must have an even vertex count. This Demonstration shows P1Fs for over 1000 graphs in Mathematica's graph database, GraphData. When "polygon view" is chosen, each Hamiltonian cycle arising from a pair of colors is shown as a polygon.
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