Dice graphs
نویسنده
چکیده
For integers n 1, a b and s let D(n; a; b; s) be the set of all lists of integers (x1; :::; xn) with a x1 ::: xn b and P xi = s. There is a graph G(n; a; b; s) with vertex-set D(n; a; b; s) in which two vertices are adjacent if one is stronger than the other in a natural dice game. In The prevalence of paradoxical dice [Bull. Inst. Combin. Appl. 45 (2005), 70-76] the dice which are isolated vertices of G(n; a; b; s) are characterized; here we prove that all the other vertices lie in a single connected component.
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