Xiong, Liming; Kužel, Roman A note on the shortness coefficient and the Hamiltonicity of 4-connected line graphs. (English) Zbl 1061.05055 Graphs Comb. 21, No. 1, 137-144 (2005). 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 Keywords:Thomassen’s conjecture; Line graph; Dominating cycle conjecture; Essentially edge connected graph; Shortness coefficient Citations:Zbl 0614.05050 PDFBibTeX XMLCite \textit{L. Xiong} and \textit{R. Kužel}, Graphs Comb. 21, No. 1, 137--144 (2005; Zbl 1061.05055) Full Text: DOI