Hamiltonian Cycles on Symmetrical Graphs
Carlo H. Séquin · 2004
The edges of highly-connected symmetrical graphs are colored so that they form Hamiltonian cycles. As an introduction we discuss the coloring of the complete graphs K 2m+1 for m>1, but the focus is on the graphs resulting from symmetrical perspective projections of the edges of the regular 4-dimensional polytopes into 3-space. The goal is to color all edges in these graphs with multiple congruent copies of Hamiltonian cycles exhibiting as much symmetry as possible. Figure 1: Map of Königsberg (a) and equivalent graph (b). 1.