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Colour number, capacity and perfectness of directed graphs.
No full textWe introduce a new concept of chromatic number for directed graphs, called the colour number and use it to upper bound the transitive clique number and the Sperner capacity of arbitrary directed graphs. Our results represent a common generalization of previous bounds of Alon and the second author and lead to a concept of perfectness for directed graphs
ON THE EXTREMAL COMBINATORICS OF THE HAMMING SPACE
No full textWe present new asymptotic bounds for problems in extremal set theory related to finding the maximum number of qualitatively 3-independent bipartitions of an n-set. We consider the space of all binary sequences of some fixed length n. As we select subsets of growing cardinality we see an increasing number of different ''small configurations'' necessarily emerge. (C) 1995 Academic Press, Inc
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