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Graphs and Combinatorics

, Volume 27, Issue 2, pp 207–214 | Cite as

On 3-Edge-Connected Supereulerian Graphs

  • Hong-Jian Lai
  • Hao Li
  • Yehong Shao
  • Mingquan ZhanEmail author
Original Paper
  • 157 Downloads

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.

Keywords

Supereulerian graphs Line graph 

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Copyright information

© Springer 2010

Authors and Affiliations

  • Hong-Jian Lai
    • 1
  • Hao Li
    • 1
  • Yehong Shao
    • 2
  • Mingquan Zhan
    • 3
    Email author
  1. 1.Department of MathematicsWest Virginia UniversityMorgantownUSA
  2. 2.Department of MathematicsOhio University Southern CampusIrontonUSA
  3. 3.Department of MathematicsMillersville UniversityMillersvilleUSA

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