Colorings of (r, r)-Uniform, Complete, Circular, Mixed Hypergraphs

In colorings of some block designs, the vertices blocks can be thought as hyperedges a hypergraph H that placed on circle and colored according to rules are related circular mixed hypergraphs. A is called if there exists host cycle vertex set X such every edge (C- or D-) induces connected subgraph this cycle. We propose an algorithm color (r,r)-uniform, complete, circular, hypergraphs for all feasible values with no gaps. doing so, we show χ(H)=2 χ¯(H)=n−s n−s−1 where s sieve number.