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- W2968141623 abstract "For a $(p, q)$-graph $G$, if the vertices of $G$ can be arranged in a sequence $v_1, v_2, ldots, v_p$ such that for each $i = 1, 2, ldots, p-1$, the distance from $v_i$ to $v_{i+1}$ equal to $k$, then the sequence is called an $AL(k)$-step traversal. Furthermore, if $d(v_p,v_1) = k$, the sequence $v_1, v_2, ldots, v_p, v_1$ is called a $k$-step Hamiltonian tour and $G$ is $k$-step Hamiltonian. In this paper we completely determine which rectangular grid graphs are 3-step Hamiltonian and show that the torus graph $C_m times C_n$ is 3-step Hamiltonian for all $m ge 3, n ge 5$." @default.
- W2968141623 created "2019-08-22" @default.
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- W2968141623 date "2019-05-02" @default.
- W2968141623 modified "2023-09-27" @default.
- W2968141623 title "A Complete Solution of 3-Hamiltonian Grids and Torus Graphs" @default.
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