摘要
Let T=(V,A)be a tournament of order n and T_i,…,T_m be diconnectedcomponents in T.If uv ∈A and P is a directed path of length k-1(k≥3)from u to v,We call P ∪{uv}a 1-antidirected cycle of length k.Let k be an integer satisfying 3≤k≤n.If every arc e∈A is contained in a 1-antidirected cycle of length k,we will refer toT as arc k 1-antidirected cyclic.If T is arc k 1-antidirected cyclic for k=3,4,…,n,T iscalled arc 1-antidirected pancyclic.In this paper,we prove that T is arc 1-antidirectedpancyclic if and only if T satisfies one of the following conditions:(i)2≤m≤3 and forany T_i,every arc e∈T_i is contained in a Hamilton path in T_i;(ii)m=1,except some spe-cial tournaments which are to be shown.
Let T=(V,A)be a tournament of order n and T_i,…,T_m be diconnected components in T.If uv ∈A and P is a directed path of length k-1(k≥3)from u to v, We call P ∪{uv}a 1-antidirected cycle of length k.Let k be an integer satisfying 3≤k ≤n.If every arc e∈A is contained in a 1-antidirected cycle of length k,we will refer to T as arc k 1-antidirected cyclic.If T is arc k 1-antidirected cyclic for k=3,4,…,n,T is called arc 1-antidirected pancyclic.In this paper,we prove that T is arc 1-antidirected pancyclic if and only if T satisfies one of the following conditions:(i)2≤m≤3 and for any T_i,every arc e∈T_i is contained in a Hamilton path in T_i;(ii)m=1,except some spe- cial tournaments which are to be shown.
基金
NSFC and YFSU
