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Optimal Algorithm of Isolated Toughness for Interval Graphs

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Parallel and Distributed Computing, Applications and Technologies (PDCAT 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12606))

Abstract

Factor and fractional factor are widely used in many fields related to computer science. The isolated toughness of an incomplete graph G is defined as \(i\tau (G)=\min \{\frac{|S|}{i(G-S)}:S\in C(G), i(G-S)>1\}\). Otherwise, we set \(i\tau (G)=\infty \) if G is complete. This parameter has a close relationship with the existence of factors and fractional factors of graphs. In this paper, we pay our attention to computational complexity of isolated toughness, and present an optimal polynomial time algorithm to compute the isolated toughness for interval graphs, a subclass of co-comparability graphs.

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Acknowledgements

This work was supported by NSFC (No.11871280), Natural Science Foundation of Zhejiang Province(China) (No. LY17A010017) and Qing Lan Project. Especially, the authors are very thankful to anonymous referees for their constructive suggestions and critical comments, which led to this improved version.

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Authors and Affiliations

  1. College of Basic Science, Ningbo University of Finance and Economics, Ningbo, 315327, Zhejiang, People’s Republic of China

    Fengwei Li & Qingfang Ye

  2. Faculty of EEMCS, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Hajo Broersma

  3. School of Mathematical Science and Institute of Mathematics, Nanjing Normal University, Nanjing, 210023, Jiangsu, People’s Republic of China

    Xiaoyan Zhang

Authors
  1. Fengwei Li
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  2. Qingfang Ye
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  3. Hajo Broersma
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  4. Xiaoyan Zhang
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Corresponding author

Correspondence to Xiaoyan Zhang .

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Editors and Affiliations

  1. Shenzhen Institutes of Advanced Technology, Shenzhen, China

    Yong Zhang

  2. Shenzhen Institutes of Advanced Technology, Shenzhen, China

    Yicheng Xu

  3. Griffith University, Gold Coast, QLD, Australia

    Hui Tian

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Li, F., Ye, Q., Broersma, H., Zhang, X. (2021). Optimal Algorithm of Isolated Toughness for Interval Graphs. In: Zhang, Y., Xu, Y., Tian, H. (eds) Parallel and Distributed Computing, Applications and Technologies. PDCAT 2020. Lecture Notes in Computer Science(), vol 12606. Springer, Cham. https://doi.org/10.1007/978-3-030-69244-5_34

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  • DOI: https://doi.org/10.1007/978-3-030-69244-5_34

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-69243-8

  • Online ISBN: 978-3-030-69244-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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