On the
k
-Component Independence Number of a Tree
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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.
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2016 ◽
Vol 116
(6)
◽
pp. 391-395
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2000 ◽
Vol 11
(03)
◽
pp. 365-371
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