On the k-Component Independence Number of a Tree
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 GS has order at most k. The k-component independence number, denoted by αckG, is the maximum order of a vertex subset that induces a subgraph with maximum com...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/5540604 |
| Summary: | 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 GS has order at most k. The k-component independence number, denoted by αckG, 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 αkT≥k/k+1n. 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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| ISSN: | 1607-887X |