Zbigniew Lonc

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We consider edge-decompositions of regular graphs into isomorphic paths. An m-PPD (perfect path decomposition) is a decomposition of a graph into paths of length m such that every vertex is an end of exactly two paths. An m-PPDC (perfect path double cover) is a covering of the edges by paths of length m such that every edge is covered exactly two times and(More)
Let H be a k-uniform hypergraph, k > 2. By an Euler tour in H we mean an alternating sequence v0, e1, v1, e2, v2, . . . , vm−1, em, vm = v0 of vertices and edges in H such that each edge of H appears in this sequence exactly once and vi−1, vi ∈ ei, vi−1 6= vi, for every i = 1, 2, . . . ,m. This is an obvious generalization of the graph theoretic concept of(More)
Let G be the set of finite graphs whose vertices belong to some fixed countable set, and let ≡ be an equivalence relation on G. By the strengthening of ≡ we mean an equivalence relation ≡s such that G ≡s H , where G,H ∈ G, if for every F ∈ G, G ∪ F ≡ H ∪ F . The most important case that we study in this paper concerns equivalence relations defined by graph(More)