Journal of the Operations Research Society of China ›› 2023, Vol. 11 ›› Issue (3): 657-666.doi: 10.1007/s40305-021-00357-6

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Remarks on Component Factors

Wei Gao1, Wei-Fan Wang2   

  1. 1. School of Information Science and Technology, Yunnan Normal University, Kunming, 650500, Yunnan, China;
    2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China
  • Received:2020-09-04 Revised:2021-02-16 Online:2023-09-30 Published:2023-09-07
  • Contact: Wei Gao, Wei-Fan Wang E-mail:gaowei@ynnu.edu.cn;wwf@zjnu.cn
  • Supported by:
    The research is partially supported by the National Natural Science Foundation of China (No. 11761083).

Abstract: In this remark, we first simply survey the important results on component factors in graphs. Then, we focus on the binding number condition of component factors in some special settings. The main contributions in this remark are two folded: (1) we reveal that the existence of some special component factors is equal to some specific binding number conditions; (2) the parameter conditions for a graph G with a $ P_{\tiny {\geqslant 3}} $-factor are determined.

Key words: $ \mathcal {H} $-factor, Component factor, Binding number

CLC Number: