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The Product of Three Cycles
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adjacent Assign the pair assume block cartesian product cells color appears coloring of G column complete bipartite graph complete graph completes the proof component coloring connected acyclic partition contradict p'(G contradicting the hypothesis corresponding cross-edges cubic graphs cut-vertex cycles H cycles in G denote disjoint edge-coloring edges in G edges of G endpoints entry follows form a partition G with less gives p'(G graph color graph G graph of order hamiltonian path hypothesis on G indicates the coloring integer Kronecker product Lemma less than n/2 Let G linking paths minimum number multiple edges n/2 sets number of hamiltonian odd endblock ordered pair orthogonal pair of colors pairs to contradict partition for G planes with copies r-factors red blue similarly skew chromatic index skew edge coloring skew Room square Subcase Suppose there exist Theorem three hamiltonian cycles unordered pairs upper bound vertex coloring vertices of G W. T. Tutte