Graphs and Combinatorics

, Volume 10, Issue 2–4, pp 249–253 | Cite as

Every 4-Connected Line Graph of a Planar Graph is Hamiltonian

  • Hong-Jian Lai


Let G be a graph withE(G) $#x2260;ø. The line graph of G, written L(G) hasE(G) as its vertex set, where two vertices are adjacent in L(G) if and only if the corresponding edges are adjacent inG. Thomassen conjectured that all 4-connected line graphs are hamiltonian [2]. We show that this conjecture holds for planar graphs.


Planar Graph Line Graph Hamilton Cycle Internal Vertex Complete Subgraph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. American Elsevier New York (1976)Google Scholar
  2. 2.
    Thomassen, C.: Reflections on graph theory, J. Graph Theory10, 309–324 (1986)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Tutte, W.T.: A theorem on planar graphs, Amer. Math. Soc.82, 99–116 (1956)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Zhan, S.M.: On hamiltonian line graphs and connectivity, Discrete Math.89, 89–95 (1991)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Hong-Jian Lai
    • 1
  1. 1.Department of MathematicsWest Virginia UniversityMorgantownUSA

Personalised recommendations