Tight toughness, isolated toughness and binding number bounds for the path factors

Abstract

For a set $\mathcal{X}$ of connected subgraphs, an $\mathcal{X}$-factor denotes a spanning subgraph D of G if each component of D is isomorphic to a member of $\mathcal{X}$. In this paper, some sufficient conditions with regard to tight toughness, isolated toughness and binding number bounds to guarantee the existence of the $\{P_2,P_7\}$-factor and $\{P_2,P_9\}$-factor for a graph are obtained.

Keywords:

• Component factor
• tight toughness
• isolated toughness
• binding number
• path

AMS:

• 05C42
• 05C38

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Supported by the Qinghai Key Laboratory of Internet of Things Project [2017-ZJ-Y21].