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A constrained colouring or, more specifically, an (α, β)-colouring of a hypergraph H, is an assignment of colours to its vertices such that no edge of H contains less than α or more than β vertices with different colours. This notion, introduced by Bujtás and Tuza, generalises both classical hypergraph colourings and more general Voloshin colourings of(More)
A degree monotone path in a graph G is a path P such that the sequence of degrees of the vertices in the order in which they appear on P is monotonic. The length (number of vertices) of the longest degree monotone path in G is denoted by mp(G). This parameter, inspired by the well-known Erd˝ os-Szekeres theorem, has been studied by the authors in two(More)
Let σ be a partition of the positive integer r. A σ-hypergraph H = H(n, r, q|σ) is an r-uniform hypergraph on nq vertices which are partitioned into n classes V1, V2, . . . , Vn each containing q vertices. An r-subset K of vertices is an edge of the hypergraph if the partition of r formed by the non-zero cardinalities |K ∩ Vi|, 1 ≤ i ≤ n, is σ. In earlier(More)
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