E. C. Milner

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It has been conjectured by Cowan and Emerson [3] that every graph has an unfriendly partition; i.e., there is a partition of the vertex set V= V, v V, such that every vertex of V, is joined to at least as many vertices in V, _, as to vertices in V,. It is easily seen that every rinite graph has such a partition, and hence by compact-ness so does any locally(More)
A tournament .T = <T,-+> is a relational structure on the non-empty set T such that for x, y e T exactly one of the three relations x->y,x=y,y->x holds. Here x-+ y expresses the fact that {x, y} e-+ and we sometimes write this in the alternative form y <-x. Extending the notation to subsets of T we write A-+ B or B <-A if a-+ b holds for all pairs a, b with(More)
For every ordinal number a, an ordered set S is called an rl,,-set if the following condition P,, is satisfied : if A and B are subsets of S, each of cardinal number less than sfi " and if a < b whenever a e A and b e B, then there exists x e S such that a < x for all a e A and x < b for all b e B. rl,,-sets were first introduced and studied by Hausdorff(More)