给定色可行集的极大混合超图

摘要

A mixed hypergraph H=(X ,C,φ)is called a bi-hypergraph if C" φ ,and the chromatic spec-trum of H is R (H)=(r 1,…,rχ),where r i(i =1,2,…,χ)is the number of strict i-colorings of H,χis theupper chromatic number of H.In this paper,we prove that there are bi-hypergrphs with certain feasible setand arbitrarily large number of bi-edges and vertices.As a result,we partially solve an open problem pro-posed by Voloshin.%若！"#，则混合超图$＝（X，！，#）称为 bi-超图。向量R（$）＝（r1，r2，…，rχ珔）表示超图$的色谱，其中ri（i＝1，2，…，珔χ）表示$的不同的严格i-染色的数目，珔χ表示$的上色数。证明了对于一个确定的可行集，存在一个 bi-超图有任意多的边数和点数，部分解决了由Voloshin提出的公开问题。