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The intersection of two Steiner triple systems $$(X,{\mathcal{A}})$$ and $$(X,{\mathcal{B}})$$ is the set $${\mathcal{A}}\cap{\mathcal{B}}$$ . The fine intersection problem for Steiner triple systems is to determine for each v, the set I(v), consisting of all possible pairs (m, n) such that there exist two Steiner triple systems of order v whose intersection $${\mathcal{I}}$$ satisfies...
In this paper, we extend the study of C4-decompositions of the complete graph with 2-regular leaves and paddings to directed versions. Mainly, we prove that if P is a vertex-disjoint union of directed cycles in a complete digraph Dv, then and Dv∪P can be decomposed into directed 4-cycles, respectively, if and only if v(v−1)−|E(P)|≡0(mod 4) and v(v−1)+|E(P)|≡0(mod 4) where |E(P)| denotes the...
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