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Characterization and Linear-Time Recognition of Paired Threshold Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12301))

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Abstract

In a paired threshold graph, each vertex has a weight, and two vertices are adjacent if and only if their weight sum is large enough and their weight difference is small enough. It generalizes threshold graphs and unit interval graphs, both very well studied. We present a vertex ordering characterization of this graph class, which enables us to prove that it is a subclass of interval graphs. Further study of clique paths of paired threshold graphs leads to a simple linear-time recognition algorithm for the graph class.

The full version of this paper, available at arXiv:1909.13029, contains all the proofs, some of which are omitted from this version due to the lack of space.

Y. Cao—Supported by RGC grants 15201317 and 15226116, and NSFC grant 61972330.

G. Rong and J. Wang—Supported by NSFC grants 61828205 and 61672536.

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Authors and Affiliations

  1. Department of Computing, Hong Kong Polytechnic University, Hong Kong, China

    Yixin Cao

  2. School of Computer Science and Engineering, Central South University, Changsha, China

    Guozhen Rong & Jianxin Wang

Authors
  1. Yixin Cao
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  2. Guozhen Rong
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  3. Jianxin Wang
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Corresponding author

Correspondence to Guozhen Rong .

Editor information

Editors and Affiliations

  1. University of Leeds, Leeds, UK

    Isolde Adler

  2. University of Leeds, Leeds, UK

    Haiko Müller

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Cao, Y., Rong, G., Wang, J. (2020). Characterization and Linear-Time Recognition of Paired Threshold Graphs. In: Adler, I., Müller, H. (eds) Graph-Theoretic Concepts in Computer Science. WG 2020. Lecture Notes in Computer Science(), vol 12301. Springer, Cham. https://doi.org/10.1007/978-3-030-60440-0_24

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  • DOI: https://doi.org/10.1007/978-3-030-60440-0_24

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  • Online ISBN: 978-3-030-60440-0

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