| Issue |
RAIRO-Oper. Res.
Volume 59, Number 5, September-October 2025
|
|
|---|---|---|
| Page(s) | 3241 - 3252 | |
| DOI | https://doi.org/10.1051/ro/2025127 | |
| Published online | 31 October 2025 | |
Some sufficient conditions for graphs to have component factors
School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, P.R. China
* Corresponding author: zsz_cumt@163.com
Received:
13
December
2024
Accepted:
10
September
2025
Let G denote a graph and k ≥ 2 be an integer. A {K1,1, K1,2, . . . , K1,k, Τ (2k + 1)}-factor of G is a spanning subgraph, whose every connected component is isomorphic to an element of {K1,1, K1,2, . . . , K1,k, Τ (2k + 1)}, where Τ (2k + 1) is a special family of trees. In this paper, we put forward some sufficient conditions for the existence of {K1,1, K1,2, . . . , K1,k, Τ (2k + 1)}-factors in graphs. Furthermore, we construct some extremal graphs to show that the main results in this paper are best possible.
Mathematics Subject Classification: 05C70 / 05C50
Key words: {K1,1, K1,2, . . . , K1,k, Τ (2k + 1)}-factor / Laplacian eigenvalue / size / degree / independence number
© The authors. Published by EDP Sciences, ROADEF, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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