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...
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| Format: | Article |
| Language: | English |
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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 |
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doaj-f3e600b9df3842ef9778f95eacb322ed2021-06-21T02:24:50ZengHindawi LimitedDiscrete Dynamics in Nature and Society1607-887X2021-01-01202110.1155/2021/5540604On the k-Component Independence Number of a TreeShuting Cheng0Baoyindureng Wu1College of Mathematics and System SciencesCollege of Mathematics and System SciencesLet 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.http://dx.doi.org/10.1155/2021/5540604 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Shuting Cheng Baoyindureng Wu |
| spellingShingle |
Shuting Cheng Baoyindureng Wu On the k-Component Independence Number of a Tree Discrete Dynamics in Nature and Society |
| author_facet |
Shuting Cheng Baoyindureng Wu |
| author_sort |
Shuting Cheng |
| title |
On the k-Component Independence Number of a Tree |
| title_short |
On the k-Component Independence Number of a Tree |
| title_full |
On the k-Component Independence Number of a Tree |
| title_fullStr |
On the k-Component Independence Number of a Tree |
| title_full_unstemmed |
On the k-Component Independence Number of a Tree |
| title_sort |
on the k-component independence number of a tree |
| publisher |
Hindawi Limited |
| series |
Discrete Dynamics in Nature and Society |
| issn |
1607-887X |
| publishDate |
2021-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2021/5540604 |
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