Hamiltonicity in connected regular graphs
نویسندگان
چکیده
In 1980, Jackson proved that every 2-connected k-regular graph with at most 3k vertices is Hamiltonian. This result has been extended in several papers. In this note, we determine the minimum number of vertices in a connected k-regular graph that is not Hamiltonian, and we also solve the analogous problem for Hamiltonian paths. Further, we characterize the smallest connected k-regular graphs without a Hamiltonian cycle.
منابع مشابه
Planar graphs, regular graphs, bipartite graphs and Hamiltonicity: Corrigendum
In [1], page 127, the third last paragraph should be replaced by: It would seem that all 3-connected cubic bipartite graphs on 30 or fewer vertices are, however, Hamiltonian. This result is claimed by Kelmans and Lomonosov, see [2].
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عنوان ژورنال:
- Inf. Process. Lett.
دوره 113 شماره
صفحات -
تاریخ انتشار 2013