Multidesigns for the graph pair formed by the 6-cycle and 3-prism

Yizhe Gao, Dan Roberts


Given two graphs G and H, a (G,H)-multidecomposition of Kn is a partition of the edges of Kn into copies of G and H such that at least one copy of each is used. We give necessary and sufficient conditions for the existence of (C66)-multidecomposition of Kn where C6 denotes a cycle of length 6 and C6 denotes the complement of C6. We also characterize the cardinalities of leaves and paddings of maximum (C66)-multipackings and minimum (C66)-multicoverings, respectively.


graph pair, decomposition, multidecomposition, packing, covering, cycle, prism

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