an:06979666
Zbl 1400.05138
Brinkmann, Gunnar; Zamfirescu, Carol T.
Grinberg's criterion
EN
Eur. J. Comb. 75, 32-42 (2019).
00421352
2019
j
05C45 05C10
Grinberg's Hamiltonicity criterion
Summary: We generalize Grinberg's Hamiltonicity criterion for planar graphs. To this end, we first prove a technical theorem for embedded graphs. As a special case of a corollary of this theorem we obtain Zaks' extension of Grinberg's criterion (which encompasses earlier work of \textit{K. R. Gehner} [Networks 6, 131--138 (1976; Zbl 0354.05039)] and \textit{Y. Shimamoto} [J. Comb. Theory, Ser. B 24, 169--180 (1978; Zbl 0395.05052)]), but the result also implies Grinberg's formula in its original form in a much broader context. Further implications are a short proof for a slightly strengthened criterion of Lewis bounding the length of a shortest closed walk from below as well as a generalization of a theorem due to \textit{J. A. Bondy} and \textit{R. H??ggkvist} [Aequationes Math. 22, 42--45 (1981; Zbl 0464.05037)].
Zbl 0354.05039; Zbl 0395.05052; Zbl 0464.05037