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On 2-Connected Spanning Subgraphs with Bounded Degree in K 1,r -Free Graphs

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Abstract

For any integer r > 1, an r-trestle of a graph G is a 2-connected spanning subgraph F with maximum degree Δ(F) ≤ r. A graph G is called K 1,r -free if G has no K 1,r as an induced subgraph. Inspired by the work of Ryjáček and Tkáč, we show that every 2-connected K 1,r -free graph has an r-trestle. The paper concludes with a corollary of this result for the existence of k-walks.

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Authors and Affiliations

  1. Department of Mathematics, University of West Bohemia, Univerzitní 8, 306 14, Plzeň, Czech Republic

    Roman Kužel & Jakub Teska

  2. Institute for Theoretical Computer Science, Charles University, Univerzitní 8, 306 14, Plzeň, Czech Republic

    Roman Kužel & Jakub Teska

Authors
  1. Roman Kužel
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  2. Jakub Teska
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Corresponding author

Correspondence to Jakub Teska.

Additional information

This research is supported by project 1M0545 and Research Plan MSM 4977751301 of the Czech Ministry of Education.

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Kužel, R., Teska, J. On 2-Connected Spanning Subgraphs with Bounded Degree in K 1,r -Free Graphs. Graphs and Combinatorics 27, 199–206 (2011). https://doi.org/10.1007/s00373-010-1011-0

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  • DOI: https://doi.org/10.1007/s00373-010-1011-0

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