Pancyclic Out-arcs of A Vertex in Local Round-decomposable Tournament
Shengjia Li · Journal of Shanxi University · 2004
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 round-decomposable and the round decomposition D=R[D_1,D_2,...,D_α],D_i is strong tournament,containing a vertex v such 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}.