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Spanning Trails with Maximum Degree at Most 4 in \(2K_2\)-Free Graphs

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Abstract

A graph is called \(2K_2\)-free if it does not contain two independent edges as an induced subgraph. Gao and Pasechnik conjectured that every \(\frac{3}{2}\)-tough \(2K_2\)-free graph with at least three vertices has a spanning trail with maximum degree at most 4. In this paper, we confirm this conjecture. We also provide examples for all \(t < \frac{5}{4}\) of t-tough graphs that do not have a spanning trail with maximum degree at most 4.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, 30303, USA

    Guantao Chen

  2. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    M. N. Ellingham & Songling Shan

  3. Department of Information Science, Nihon University, Tokyo, 156-8550, Japan

    Akira Saito

Authors
  1. Guantao Chen
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  2. M. N. Ellingham
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  3. Akira Saito
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  4. Songling Shan
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Corresponding author

Correspondence to Songling Shan.

Additional information

M. N. Ellingham: Supported by Simons Foundation award 429625.

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Chen, G., Ellingham, M.N., Saito, A. et al. Spanning Trails with Maximum Degree at Most 4 in \(2K_2\)-Free Graphs. Graphs and Combinatorics 33, 1095–1101 (2017). https://doi.org/10.1007/s00373-017-1823-2

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  • DOI: https://doi.org/10.1007/s00373-017-1823-2

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