中文摘要：

本文利用多重插入法，对局部内（外）半完全有向图及其扩张有向图的可迹性作了讨论．首先，证明了对n阶连通的局部内半完全有向图D，若它中任意不相邻的受控点对{x，y）满足d（x）≥n-1，d（9）≥n-2，或d（z）≥n-2，d（y）≥n-1，则D是可迹的．同时还证明了对n阶连通的局部内半完全有向图D，若它中任意不相邻的受控点对{x，y）有min{d＋（x）＋d-（y），d-（x）＋d＋（g）}≥n-1，D是可迹的．其次，证明了n阶连通的扩张局部内半完全有向图D，如果任意不相邻的控制点对{u，v）和任意不相邻的受控点对（x，y）同时满足（1）d（u）≥n-1，d（v）≥n-1；（2）d（x）≥n-1，d（9）≥n-2或d（x）≥n-2，d（y）2n-1，则D是可迹的．最后，利用逆图的性质把这三个结论推广到n阶连通的局部外半完全有向图与n阶连通的扩张局部外半完全有向图中．

英文摘要：

In this paper, we study the traceability of locally in（out）-semicomplete digraphs and extended locally in（out）-semicomplete digraphs by multi-insertion technique we show that for a connected locally in-semicomplete digraph D of order n, if for First, every we show that for a connected locally in-semicomplete digraph D of order n, if for everydominated pair of non-adjacent vertices {x, y}, either d（x） ≥ n - 1 and d（y）≥ n - 2, or d（x）≥ n- 2 and d（y） ≥ n- 1, then D is traceable. At the same time, we show for a connected locally in-semicomplete digraph D of order n, if for every dominated pail of non-adjacent vertices {x, y}, min{d＋（x） ＋ d-（y）, d-（x） ＋ d＋（y）} 〉 n- 1, then D is traceable. Second, we show that for a connected extended locally in-semicomplete digraph D of order n, if D is satisfied with the following two conditions： （1） for every dominated pair of non-adjacent vertices {u,v}, d（u） 〉 n - 1, d（v） 〉 n - 1; （2） for every dominated pair of non-adjacent vertices {x,y}, either d（x） 〉 n - 1 and d（y） ≥ n - 2 or d（x）≥ n - 2 and d（y） 〉 n - 1, then D is traceable. Finally, by the properties of reversing digraphs, we generalize these three results to locally out-semicomplete digraphs and extended locally out-semicomplete digraphs.