Colouring 4-cycle systems with equitably coloured blocks

Uniform coloured hypergraphs and blocking sets

“…Similar conditions can be found also for chromatic indices and can be applied to study the problems examined in [5,8,14,16,18].…”

“…Given a graph G, a Gdesign is a pair Σ = (X; B), where X is a finite non empty set and B is a family of graphs, all isomorphic to G, such that every pair of distinct elements of X is an edge of exactly λ graphs of B. For G-designs there is an interesting literature about existence problems and also about colourings [1,5,8,14,16,18,21].…”

On some colouring of 4-cycle systems with specified block colour patterns

“…This contains at least one pair of non-adjacent vertices in the same colour class, which must occur as adjacent vertices in some other 4-cycle. Type cd colouring is studied in [2]. We deal here with type S colourings where S ⊆ {c, d, e, f } and |S| 3.…”

“…are strict colourings in the sense of Voloshin [8] in which each block contains at least two vertices having the same colour and at least two vertices with a different colour. A further step is taken by Milici et al [5] where the authors consider some types of colouring of Steiner systems S (2, 3, v) and S (2,4, v) (K 3 -designs and K 4 -designs in our terminology) in which only specified block colouring patterns are allowed.…”

Block colourings of 6-cycle systems

“…Block colourings for s = 2, s = 3 and s = 4 of 4CS have been studied in [3,9,11]. The problem arose as a consequence of colourings of Steiner systems studied in [7,10,12,18]. For further references on such topics see [2,5,14,19].…”