The edge coloring number of generalized completer-partitioned hypergraph

A hypergraph H is said to be a generalized complete r-partitioned hypergraph, denoted by Ktn11,t,n22,,……,t,rnr. If its vertex set X endows with a partition X1, X2, …, Xr, i.e., for all i≠j, Xi∩Xj=∅(1≤i,j≤r), X=∪ri=1Xi, |Xi|=ni(1≤i≤r). The edge set E consists of all distinct subsets E′ of X such that |E′∩Xi|=ti(1≤ti≤ni,1≤i≤r). This article considers the edge coloring number of generalized completer-partitioned hypergraph. Based on the edge coloring of complete r-partite hypergraph and complete t-uniform hypergraph,the edge chromatic number of special generalized complete r-partitioned hypergraph has been found. The upper bound on the edge chromatic number of generalized complete r-partitioned hypergraph is given, which extends edge chromatic number in complete r-partite hypergraph and complete t-uniform hypergraph.