Issue |
RAIRO-Oper. Res.
Volume 57, Number 3, May-June 2023
|
|
---|---|---|
Page(s) | 1443 - 1451 | |
DOI | https://doi.org/10.1051/ro/2023078 | |
Published online | 21 June 2023 |
Degree conditions for path-factor critical deleted or covered graphs
School of Mathematics and Information Sciences, Yantai University, Yantai, Shandong 264005, P.R. China
* Corresponding author: liuhongxia@ytu.edu.cn
Received:
3
February
2023
Accepted:
29
May
2023
A path-factor of a graph G is a spanning subgraph of G whose components are paths. A P≥d-factor of a graph G is a path-factor of G whose components are paths with at least d vertices, where d is an integer with d ≥ 2. A graph G is P≥d-factor covered if for any e ∈ E(G), G admits a P≥d-factor including e. A graph G is (P≥d, n)-factor critical deleted if for any Q ⊆ V(G) with |Q| = n and any e ∈ E(G − Q), G – Q − e has a P≥d-factor. A graph G is (P≥d, n)-factor critical covered if for any Q ⊆ V(G) with |Q| = n, G − Q is a P≥d-factor covered graph. In this paper, we verify that (1) an (n + t + 2)-connected graph G of order p with p ≥ 4t + n + 7 is (P≥3, n)-factor critical deleted if max for any independent set {v1, v2, …, v2t+1} of G, where n and t are two nonnegative integers with t ≥ 1; (2) an (n + t + 1)-connected graph G of order p with p ≥ 4t + n + 5 is (P≥3, n)-factor critical covered if max
for any independent set {v1, v2, …, v2t+1} of G, where n and t are two nonnegative integers with t ≥ 1.
Mathematics Subject Classification: 05C70 / 05C38
Key words: Graph / Degree condition / P≥3-factor / (P≥3, n)-factor critical deleted graph / (P≥3, n)-factor critical covered graph
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
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