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On 3-Edge-Connected Supereulerian Graphs

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Abstract

The supereulerian graph problem, raised by Boesch et al. (J Graph Theory 1:79–84, 1977), asks when a graph has a spanning eulerian subgraph. Pulleyblank showed that such a decision problem, even when restricted to planar graphs, is NP-complete. Jaeger and Catlin independently showed that every 4-edge-connected graph has a spanning eulerian subgraph. In 1992, Zhan showed that every 3-edge-connected, essentially 7-edge-connected graph has a spanning eulerian subgraph. It was conjectured in 1995 that every 3-edge-connected, essentially 5-edge-connected graph has a spanning eulerian subgraph. In this paper, we show that if G is a 3-edge-connected, essentially 4-edge-connected graph and if for every pair of adjacent vertices u and v, d G (u) + d G (v) ≥ 9, then G has a spanning eulerian subgraph.

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Authors and Affiliations

  1. Department of Mathematics, West Virginia University, Morgantown, WV, 26506, USA

    Hong-Jian Lai & Hao Li

  2. Department of Mathematics, Ohio University Southern Campus, Ironton, OH, 45638, USA

    Yehong Shao

  3. Department of Mathematics, Millersville University, Millersville, PA, 17551, USA

    Mingquan Zhan

Authors
  1. Hong-Jian Lai
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  2. Hao Li
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  3. Yehong Shao
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  4. Mingquan Zhan
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Corresponding author

Correspondence to Mingquan Zhan.

Additional information

Research is supported by the Millersville University Faculty Released-Time grant.

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Lai, HJ., Li, H., Shao, Y. et al. On 3-Edge-Connected Supereulerian Graphs. Graphs and Combinatorics 27, 207–214 (2011). https://doi.org/10.1007/s00373-010-0974-1

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  • DOI: https://doi.org/10.1007/s00373-010-0974-1

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