In a previous article the authors showed that almost all labelled cubic graphs are hamiltonian. In the present article, this result is used to show that almost all r ‐regular graphs are hamiltonian for any fixed r ⩾ 3, by an analysis of the distribution of 1‐factors in random regular graphs. Moreover, almost all such graphs are r ‐edge‐colorable if they have an even number of vertices. Similarly, almost all r ‐regular bipartite graphs are hamiltonian and r ‐edge‐colorable for fixed r ⩾ 3.
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Robinson et al. (1994) studied this question.