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- W1559700736 abstract "1 An extremal problem on labelled directed trees A tree F is called a directed tree, if there is a direction on the edges, so that a vertex v0 (root) has only out-neighbours, and an arbitrary vertex v 6=v0 has a uniquely determined in-neighbour n(v). N(v) denotes the out-neighbourhood of v. The set of the leaves of a tree F is denoted by `(F ). Let U be a (finite) set. A tree F = F (U) is called labelled, if a subset A(v) of U is associated with each vertex v of F . For fixed integers k ≥ 1, ` ≥ 2 and U = {1, 2, ...,m} consider the family of labelled directed trees F (m) k,` , for which the vertices of each tree F ∈ F (m) k,` are labelled as follows. The label of the root v0 of F is A(v0) = U . For an arbitrary vertex v of F there is a disjoint partition N(v) = ⋃` i=1Ni(v) of its out-neighbourhood satisfying the following properties." @default.
- W1559700736 created "2016-06-24" @default.
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- W1559700736 date "2005-01-01" @default.
- W1559700736 modified "2023-09-27" @default.
- W1559700736 title "An extremal problem on labelled directed trees and applications to database theory" @default.
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