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Saturation Numbers for Linear Forests\(P_5 \cup tP_2\)

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Abstract

A graph \(G\) is \(F\)-saturated if it has no \(F\) as a subgraph, but does contain \(F\) after the addition of any new edge. The saturation number, \(sat(n,F)\), is the minimum number of edges of a graph in the set of all \(F\)-saturated graphs with order \(n\). In this paper, we determine the saturation number \(sat(n,P_5\cup tP_2)\) for \(n\ge 3t+8\) and characterize the extremal graphs for \(n>(18t+76)/5\).

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Acknowledgments

The authors would like to thank the referees for their helpful comments and suggestions leading to an improvement of our paper.

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Authors and Affiliations

  1. School of Automation, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China

    Qiong Fan

  2. Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, People’s Republic of China

    Qiong Fan & Chunxiang Wang

Authors
  1. Qiong Fan
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  2. Chunxiang Wang
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Correspondence to Qiong Fan.

Additional information

Supported by the National Natural Science Foundation of China under Grants 11171129, 11271149, and 11371162, and by the Self-determined Research Funds of CCNU from the colleges basic research and operation of MOE.

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Fan, Q., Wang, C. Saturation Numbers for Linear Forests\(P_5 \cup tP_2\) . Graphs and Combinatorics 31, 2193–2200 (2015). https://doi.org/10.1007/s00373-014-1514-1

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  • DOI: https://doi.org/10.1007/s00373-014-1514-1

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