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An Improved Kernel and Parameterized Algorithm for Almost Induced Matching

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Theory and Applications of Models of Computation (TAMC 2024)

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Abstract

An induced subgraph is called an induced matching if each vertex is a degree-1 vertex in the subgraph. The Almost Induced Matching problem asks whether we can delete at most k vertices from the input graph such that the remaining graph is an induced matching. This paper studies parameterized algorithms for this problem by taking the size k of the deletion set as the parameter. First, we prove a 6k-vertex kernel for this problem, improving the previous result of 7k. Second, we give an \(O^*(1.6765^k)\)-time and polynomial-space algorithm, improving the previous running-time bound of \(O^*(1.7485^k)\).

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 62372095 and 62172077) and the Sichuan Natural Science Foundation (Grant No. 2023NSFSC0059).

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Authors and Affiliations

  1. University of Electronic Science and Technology of China, Chengdu, China

    Yuxi Liu & Mingyu Xiao

Authors
  1. Yuxi Liu
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  2. Mingyu Xiao
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Correspondence to Mingyu Xiao .

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Editors and Affiliations

  1. Chinese Academy of Sciences, Beijing, China

    Xujin Chen

  2. The Hong Kong Polytechnic University, Hong Kong, China

    Bo Li

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Liu, Y., Xiao, M. (2024). An Improved Kernel and Parameterized Algorithm for Almost Induced Matching. In: Chen, X., Li, B. (eds) Theory and Applications of Models of Computation. TAMC 2024. Lecture Notes in Computer Science, vol 14637. Springer, Singapore. https://doi.org/10.1007/978-981-97-2340-9_8

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  • DOI: https://doi.org/10.1007/978-981-97-2340-9_8

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  • Print ISBN: 978-981-97-2339-3

  • Online ISBN: 978-981-97-2340-9

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