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A note on the shortness coefficient and the Hamiltonicity of 4-connected line graphs. (English) Zbl 1061.05055

Summary: C. Thomassen [J. Graph Theory 10, 309–324 (1986; Zbl 0614.05050)] proposed a well-known conjecture: every 4-connected line graph is Hamiltonian. In this note, we show that Thomassen’s conjecture is equivalent to the statement that the shortness coefficient of the class of all 4-connected line graphs is one and the statement that the shortness coefficient of the class of all 4-connected claw-free graphs is one respectively.

MSC:

05C45 Eulerian and Hamiltonian graphs
05C35 Extremal problems in graph theory

Citations:

Zbl 0614.05050
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