The upper chromatic number <(chi)over bar>(H) of a set system H is the maximum number of colours that can be assigned to the elements of the underlying set of H in such a way that each H is an element of H contains a monochromatic pair of elements. We prove that a Steiner triple system of order upsilon less than or equal to 2(k)-1 has an upper chromatic number which is at most k. This bound is the best possible, and the extremal configurations attaining equality can be characterized. Some consequences for Steiner quadruple systems are also obtained.
Upper chromatic number of Steiner triple and quadruple systems
MILAZZO, Lorenzo Maria Filippo;
1997-01-01
Abstract
The upper chromatic number <(chi)over bar>(H) of a set system H is the maximum number of colours that can be assigned to the elements of the underlying set of H in such a way that each H is an element of H contains a monochromatic pair of elements. We prove that a Steiner triple system of order upsilon less than or equal to 2(k)-1 has an upper chromatic number which is at most k. This bound is the best possible, and the extremal configurations attaining equality can be characterized. Some consequences for Steiner quadruple systems are also obtained.File in questo prodotto:
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