On The Spanning Connectivity Of Tournaments

In this paper,we define the spanning connectivity of digraphs,generalize the weak Hamil-tonian connectedness of tournaments,and study the spanning connectivity of tournaments.We also study the existence of specified cycles in bipartite tournaments.We have got some meaningful results.The overall structure of this paper is as follows:In Chapter 1,we mainly introduce the research background of this paper,and system-atically expound the research status of spanning connectivity and cycle structure.Then we put forward the problems and give the related results in this paper.In Chapter 2,we study the spanning connectivity of tournaments.We define the spanning connectivity of digraphs and get the following main results:(1)for k? 0,a(2k + 1)-strong tournament is(k + 2)*-weakly connected.(2)for k? 2,a 2k-strong tournament is k*-strongly connected.(3)In a tournament with n vertices and irregularity i(T)?k,if n ? 6t + 5k(t ? 2),then ks*(T)? t;if n ? 6t + 5k-3(t ? 2),then kw*(T)? t + 1.In Chapter 3,we study the existence of specified cycles in bipartite tournaments.We define the decomposable k-regular bipartite tournament by induction and get the following main results:a decomposable k-regular(k ? 3)bipartite tournament BT4k contains D(4k,p)for 2<p<4k unless BT4k is isomorphic to a digraph D which has a Hamiltonian cycle(1,2,3,...,4k,1),for any vertex i?(1,2,3,...,4k,1),there are(4m + i-1,i)E A(D)and(i,4m + i + 1)E A(D),where 1 ? m ? k-1,every vertex i modulo 4k so that the vertex 4k + i is the vertex i.