Search

Let G be a graph and k ≥ 1 be an integer. A subset S of vertices in a graph G is called a k -component independent set of G if each component of G S has order at most k. The k -component independence number, denoted by α c k G , is the maximum order of a vertex subset that induces a subgraph with maximum component order at most k. We prove that if a tree T is of order n , then α k T ≥ k / k + 1 n. The bound is sharp. In addition, we give a linear-time algorithm for finding a maximum k -component independent set of a tree. [ABSTRACT FROM AUTHOR]