Abstract
Given two disjoint sets of k vertices each in a graph G, it was recently asked whether \(\delta (G) \ge n/2\) and \(\kappa (G) \ge 2k\) would be a sufficient assumption to guarantee the existence of a Hamiltonian cycle of G which alternates visiting vertices of the two selected sets. We answer this question in the affirmative when the graph is large and we also provide a generalization to more sets.
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Funding
Supported by the National Science Foundation of China (nos. 11601254, 11551001, 11161037, and 11461054) and the Science Found of Qinghai Province (nos. 2016-ZJ-948Q, and 2014-ZJ-907).
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Dedicated to the memory of Ralph Faudree, whose life and work inspired this and many other researchers.
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Magnant, C., Mao, Y. On Cycles that Alternate Through Selected Sets of Vertices. Graphs and Combinatorics 36, 1517–1523 (2020). https://doi.org/10.1007/s00373-020-02190-9
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DOI: https://doi.org/10.1007/s00373-020-02190-9