Supereulerian Digraphs With Forbidden Induced Subdigraph

Through the study and understanding of the properties of the Supereulerian digraph,the finding of the Supereulerian digraph,the decision condition of the Mycielskian(di)graph with the forbidden-induced digraph and the Supereulerian of the digraph are given.Starting from the properties of Euler digraph and the Supereulerian digraph,we obtain the Supereulerian digraph,and the Supereulerian digraph must included the Euler digraph.The research on the related problems of Euler's graph and Euler digraph is very extensive and in-depth.Of course,the study of the Euler digraph has already entered the field of experts and scholars,and has drawn many important conclusions.The research on the problem of the Supereulerian digraph has become a very important problem in graph theory.The text of this paper is divided into three parts:The first part,the research background and the research status at home and abroad of the Euclidean directed graph are given firstly;Secondly,some basic concepts are introduced,including the given family F(?,h),P4',P4",handle,Mycielskian diagraph,etc.Finally,the paper lists the important research results.The second part,according to the definition of F(?,h),and we determine the smallest value h4'(h4")such that for any h'(h")no less than h4'(h4"),every digraph in F(P4',h')(F(P4",h"))is supereulerian.At last,a strong digraph of order at least 3 without containing an induced subdigraph is supereulerian digraph.The third part,we mainly study the Eulerian and Supereulerian of the Mycielskian of graphs and digraphs,respectively.