Grinberg’s Criterion on Non-Planar Graphs
نویسندگان
چکیده
Robertson (1968) and independently, Bondy (1972) proved that the generalized Petersen graph P (n, 2) is non-hamiltonian if n ≡ 5 (mod 6) while Thomason (1982) proved that it has precisely three hamiltonian cycles if n ≡ 3 (mod 6). Here we give a unified proof (which is easier) of these results using Grinberg’s theorem.
منابع مشابه
Planar hypohamiltonian graphs
A graph is called hypohamiltonian if it is not hamiltonian but, when omitting an arbitrary vertex, it becomes hamiltonian. The smallest hypohamiltonian graph is the famous Petersen graph (found by Kempe in 1886) on 10 vertices. In 1963, Sousselier posed a problem of recreational nature, and thus began the study of hypohamiltonian graphs. Many authors followed, in particular Thomassen with a ser...
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