“…The t K 3 's in a t-foil or a t-foiloid are denoted in order like sequence. (1,4,8), (1,5,9), (1,6,10), (1,3,7), (1,4,8), (1,5,9), (1,6,10)].…”
Section: Balanced Quatrefoil Decomposition Of Complete Multigraphsmentioning
confidence: 99%
“…Problem [1]. To solve this problem, a cost allocation problem and a split delivery vehicle routing problem have been studied [3], [4], [7]. Recently, Ushio and Fujimoto [10], [11] considered the complete tripartite graph and the complete graph and took a foil as a simple model of the routing tour.…”
We show that the necessary and sufficient condition for the existence of a balanced quatrefoil decomposition of the complete multigraph λK n is n ≥ 9 and λ(n − 1) ≡ 0 (mod 24). Decomposition algorithms are also given.
“…The t K 3 's in a t-foil or a t-foiloid are denoted in order like sequence. (1,4,8), (1,5,9), (1,6,10), (1,3,7), (1,4,8), (1,5,9), (1,6,10)].…”
Section: Balanced Quatrefoil Decomposition Of Complete Multigraphsmentioning
confidence: 99%
“…Problem [1]. To solve this problem, a cost allocation problem and a split delivery vehicle routing problem have been studied [3], [4], [7]. Recently, Ushio and Fujimoto [10], [11] considered the complete tripartite graph and the complete graph and took a foil as a simple model of the routing tour.…”
We show that the necessary and sufficient condition for the existence of a balanced quatrefoil decomposition of the complete multigraph λK n is n ≥ 9 and λ(n − 1) ≡ 0 (mod 24). Decomposition algorithms are also given.
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