| Issue |
RAIRO-Oper. Res.
Volume 57, Number 5, September-October 2023
|
|
|---|---|---|
| Page(s) | 2465 - 2471 | |
| DOI | https://doi.org/10.1051/ro/2023147 | |
| Published online | 29 September 2023 | |
Sufficient conditions for graphs to have strong parity factors
1
School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, P.R. China
2
School of Science, Dalian Jiaotong University, Dalian, Liaoning 116028, P.R. China
* Corresponding author: zhangyuli_djtu@126.com
Received:
5
June
2023
Accepted:
9
September
2023
A graph G has a strong parity factor F if for every subset X ⊆ V (G) with |X| even, G contains a spanning subgraph F such that δ(F) ≥ 1, dF (u) ≡ 1 (mod 2) for any u ∈ X, and dF(v) ≡ 0 (mod 2) for any v ∈ V(G) \ X. In this article, we first provide a size condition for a graph having a strong parity factor. Then we put forward a toughness condition to guarantee that a graph has a strong parity factor.
Mathematics Subject Classification: 05C70
Key words: Graph / size / toughness / strong parity factor
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
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