On a conjecture concerningk-Hamilton-nice sequences期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On a conjecture concerningk-Hamilton-nice sequences

Authors:	Yiping Liu Zhengsheng Wu

Affiliation:	(1) Department of Mathematics, Nanjing Normal University, 210024 Nanjing, China

Abstract:	In this paper, we prove that a non-negative rational number sequence (a₁,a₂, ...,a_k+1) isk-Hamilton-nice, if (1)a_k+12, and (2) _j^=1/h (i_j–1)k–1 implies $sumnolimits_{j = 1}^h {(a_{i_j } - 1)} leqslant 1$ for arbitraryi₁,i₂,...i_h {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.This project is supported by the National Natural Science Foundation of China.

Keywords:	Hamiltonian graph k-Hamilton-nice k-Hamilton-nice sequence
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