Fibres and ordered set coloring
نویسندگان
چکیده
A Jbre F of a partially ordered set P is a subset which intersects each nontrivial maximal antichain of P. Let I be the smallest constant such that each finite partially ordered set P contains a fibre of size at most I ‘1 PI. We show that 1, < 3 by finding a good 3-coloring of the nontrivial antichains of P. Some decision problems involving iibres are also considered. For instance, it is shown that the problem of deciding if a partially ordered set has a fibre of size at most k is NP-hard.
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 58 شماره
صفحات -
تاریخ انتشار 1991