Volume 54, Number 6, November-December 2020
|Page(s)||1827 - 1834|
|Published online||16 September 2020|
Remarks on path factors in graphs
School of Science, Jiangsu University of Science and Technology, Mengxi Road 2, 212003 Zhenjiang, Jiangsu, P.R. China
* Corresponding author: firstname.lastname@example.org
Accepted: 20 November 2019
A spanning subgraph of a graph is defined as a path factor of the graph if its component are paths. A P≥n-factor means a path factor with each component having at least n vertices. A graph G is defined as a (P≥n, m)-factor deleted graph if G–E′ has a P≥n-factor for every E′ ⊆ E(G) with |E′| = m. A graph G is defined as a (P≥n, k)-factor critical graph if after deleting any k vertices of G the remaining graph of G admits a P≥n-factor. In this paper, we demonstrate that (i) a graph G is (P≥3, m)-factor deleted if κ(G) ≥ 2m + 1 and bind(G) ≥ 2/3 - ; (ii) a graph G is (P≥3, k)-factor critical if κ(G) ≥ k + 2 and bind(G) ≥ .
Mathematics Subject Classification: 05C70 / 05C38 / 90B10
Key words: Graph / path factor / binding number / connectivity
© EDP Sciences, ROADEF, SMAI 2020
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