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- W302890624 abstract "Alspach and Qin proved that connected Cayley graphs of Hamiltonian groups (all subgroups are normal) are either Hamilton-connected (every pair of vertices is joined by a Hamilton path), or are bipartite and Hamilton-laceable (every pair on opposite sides of the bipartition are joined by a Hamilton path). Their proof made use of Hamilton-connectedness of certain Generalized Petersen graphs.In this work, we extend (and make a small correction to) the results of Alspach and Liu on Hamilton paths in generalized Petersen graphs. Alspach and Liu showed that, for k∈{1,2,3} and gcd(n,k)=1, P(n,k) is either Hamilton-connected or bipartite and Hamilton-laceable, as long as (n,k)≠(6r+5,2) or (5,3). For k=2, we consider the remaining cases for n and completely determine which pairs of vertices in P(n,2) are joined by Hamilton paths. However, the main point is to show that, for each k, it is a finite problem to determine, for all n, which pairs of vertices in P(n,k) are the ends of a Hamilton path." @default.
- W302890624 created "2016-06-24" @default.
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- W302890624 date "1940-12-01" @default.
- W302890624 modified "2023-09-26" @default.
- W302890624 title "Statistical mechanics" @default.
- W302890624 doi "https://doi.org/10.1016/s0016-0032(40)90845-6" @default.
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