Graphs and Combinatorics

, Volume 27, Issue 2, pp 207–214

On 3-Edge-Connected Supereulerian Graphs

Original Paper

DOI: 10.1007/s00373-010-0974-1

Cite this article as:
Lai, HJ., Li, H., Shao, Y. et al. Graphs and Combinatorics (2011) 27: 207. doi:10.1007/s00373-010-0974-1


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, dG(u) + dG(v) ≥ 9, then G has a spanning eulerian subgraph.


Supereulerian graphsLine graph

Copyright information

© Springer 2010

Authors and Affiliations

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