圆可分解的局部竞赛图中的点外弧泛圈问题

摘要

Yao Tianxing(Discrete Appl.Math.,2000,99:245-249)已经证明了每一个强连通竞赛图都包含点,它的每条外弧都是泛圈的.将此结论推广到强连通的圆可分解的严格局部竞赛图,并证明了每一个强连通的圆可分解的严格局部竞赛图D,它的圆分解是D=R[D1,D2,…,Dα],其中Di,i=1,2,…,α是强连通竞赛图,那么D包含一个点v,它的每条外弧是(g+1)-泛圈的,g=max{l(Ca)|Ca是包含a的最长诱导圈,a∈V(R),l(Ca)是Ca的长度}.%Yao Tianxing (Discrete Appl. Math., 2000, 99: 245-249)has proved that every strong tournament contains a vertex v such that each arc going out from the vertex is pancyclic. In this paper,the result is extended to strong round-decomposable proper local tournament and prove that a strong local tournament D,which is roundsuch that every arc going out from v is (g+ 1)-panaydic,where g = {l (Ca)| Ca is the longest induced cycle containing a,a ∈ V (R), where l(Ca ) is the length of Ca }.