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Tank-Ring Factors in Supereulerian Claw-Free Graphs

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Abstract

A graph G has a tank-ring factor F if F is a connected spanning subgraph with all vertices of degree 2 or 4 that consists of one cycle C and disjoint triangles attaching to exactly one vertex of C such that every component of G − C contains exactly two vertices. In this paper, we show the following results. (1) Every supereulerian claw-free graph G with 1-hourglass property contains a tank-ring factor. (2) Every supereulerian claw-free graph with 2-hourglass property is Hamiltonian.

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Authors and Affiliations

  1. School of Software Technology, Dalian University of Technology, Dalian, Liaoning, 116620, People’s Republic of China

    MingChu Li, Lifeng Yuan & He Jiang

  2. Department of Mathematics, Shenyang Polyechnic College, Shenyang, 110045, People’s Republic of China

    Bing Liu

  3. Department of Computer Science, University of Durham, Durham, DH1 3LE, UK

    H. J. Broersma

Authors
  1. MingChu Li
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  2. Lifeng Yuan
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  3. He Jiang
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  4. Bing Liu
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  5. H. J. Broersma
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Corresponding author

Correspondence to He Jiang.

Additional information

Supported by Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) under grant No.: 200801410028 by Nature Science Foundation Project of Liaoning under Grant No.: 2201102038, and by Nature Science foundation of China (NSFC) under Grant No.: 61175062, 61100194.

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Li, M., Yuan, L., Jiang, H. et al. Tank-Ring Factors in Supereulerian Claw-Free Graphs. Graphs and Combinatorics 29, 599–608 (2013). https://doi.org/10.1007/s00373-011-1117-z

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  • DOI: https://doi.org/10.1007/s00373-011-1117-z

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