Abstract
In this paper, we prove that a non-negative rational number sequence (a1,a2, ...,ak+1) isk-Hamilton-nice, if (1)ak+1≤2, and (2) σj=1/h (ij−1)≤k−1 implies\(\sum\nolimits_{j = 1}^h {(a_{i_j } - 1)} \leqslant 1\) for arbitraryi1,i2,...ih e {1,2,... ,k}. This result was conjectured by Guantao Chen and R.H. Schelp, and it generalizes several well-known sufficient conditions for graphs to be Hamiltonian.
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