科研之友
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摘要
The detour order of a graph G, denoted by tau (G), is the order of a longest path in G. A subset S of V(C) is called a P(n)-kernel of G if tau(G[S]) <= n - 1 and every vertex nu is an element of V(C) - S is adjacent to an end-vertex of a path of order n - 1 in B[S]. A partition of the vertex set of G into two sets. A and B, such that tau(G[A]) <= a and tau(G[B]) <= b is called an (a, b)-partition of G. In this paper we show that any graph with girth g has a P(n+1)-kernel for every n < (3g)/(2) - 1. Furthermore, if tau(G) = a + b, 1 <= a <= b, and G has girth greater than (2)/(3) (a + 1), then G has an (a, b)-partition.
- 出版日期2010-11-6
- 单位河北工业大学
