Complex uniformly resolvable decompositions of K v

2021 
In this paper we consider complex uniformly resolvable decompositions of the complete graph K v into subgraphs such that each resolution class contains only blocks isomorphic to the same graph from a given set ℋ and at least one parallel class is present from each graph of ℋ . We completely determine the spectrum for the cases ℋ = { K 2 ,  P 3 ,  K 3 } , ℋ = { P 4 ,  C 4 } , and ℋ = { K 2 ,  P 4 ,  C 4 } .
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