Balanced Bowtie and Trefoil Decomposition of Complete Tripartite Multigraphs(Graphs and Networks)(Regular Section)

概要

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First, we show that the necessary and sufficient condition for the existence of a balanced bowtie decomposition of the complete tripartite multi-graph λΚ_<n1, n2, n3> is (i)n_1=n_2=n_3┴0(mod 6) for λ┴1, 5(mod 6), (ii)n_1=n_2=n_3┴0(mod 3) for λ┴2, 4(mod 6), (iii)n_1=n_2=n_3┴0(mod 2) for λ┴3(mod 6), and (iv)n_1=n_2=n_3≥2 for λ┴0(mod 6). Next, we show that the necessary and sufficient condition for the existence of a balanced trefoil decomposition of the complete tripartite multi-graph λΚ_<n_1, n_2n_3> is (i)n_1=n_2=n_3┴0(mod 9) for λ┴1, 2, 3, 5, 7, 8(mod 9), (ii)n_1=n_2=n_3┴0(mod 3) for λ┴3, 6(mod 9), and (iii)n_1=n_2=n_3≥3 for λ┴0(mod 9).
社団法人電子情報通信学会の論文
2001-03-01