广义r-部完全超图的边色数

The edge coloring number of generalized complete r-partitioned hypergraph

研究了广义r-部完全超图的边色数的问题.在r-部完全超图与t-一致完全超图的着色基础上,确定一类特殊的广义r-部完全超图的边色数,对一般的广义r-部完全超图的边色数给出了上界,推广了r-部完全超图与t-一致完全超图的着色结论.

A hypergraph H is said to be a generalized complete r-partitioned hypergraph,denoted by K（n1,n2,…,nr）（t1,t2,…,tr）.If its vertex set Xendows with a partition X1,X2,…,Xr,i.e.,for all i≠j,Xi∩Xj=？（1≤i,j≤r）,X=r∪（i=1） Xi,｜Xi｜=ni（1≤i≤r）.The edge set Econsists of all distinct subsets E′of Xsuch that｜E′∩Xi｜=ti（1≤ti≤ni,1≤i≤r）.This article considers the edge coloring number of generalized complete r-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.