Kaiser and Vrana [European J. Combin. 33 (2012), 924-947] showed that every 5-connected line graph of minimum degree at least 6 is hamiltonian, which gives a partial solution to Thomassen’s Conjecture on hamiltonicity of line graphs [J. Graph Theory 10 (1986), 309-324]. In this paper, we prove that every 5-connected line graph of sufficiently large order compared with a given positive integer k and of minimum degree at least 6 also has a 2-factor with exactly k cycles. In order to show this result, we investigate minimum degree conditions for the existence of such a 2-factor in hamiltonian line graphs.
|Number of pages||6|
|Journal||Acta Mathematica Universitatis Comenianae|
|Publication status||Published - 2019 Sep 2|
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