A Problem of Maximum Consistent Subsets


By: Raymond E. Miller, David E. Muller

Published in: RC240 in 2008

(i) No subset Si, is contained in any other subset Sj.
(ii) If T i s a subset of N such that each pair of integers r, s contained in T is also contained in same S of C, then T itself is contained in at least one S of C.

The problem is formulated as one in linear graphs, various properties resulting from the graphical formulation are investigated, and a method of constructing a class of subsets is given and proved to be maximum. The maximum cardinality p is shown to be 3k when n = 3k, 2 . 3k-1 when n = 3k-1, and 4 . 3k-1 when n = 3k + 1.


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