- Title
- Sufficient Conditions for a Graph to Have All [a, b]-Factors and (a, b)-Parity Factors
- Creator
- Yang, Zixuan; Zhang, Xuechun; Lu, Hongliang; Lin, Yuqing
- Relation
- Bulletin of the Malaysian Mathematical Sciences Society Vol. 45, Issue 4, p. 1657-1667
- Publisher Link
- http://dx.doi.org/10.1007/s40840-022-01281-5
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 2022
- Description
- Let G be a graph with vertex set V and let b> a be two positive integers. We say that G has all [a, b]-factors if G has an h-factor for every h: V→ N such that a≤ h(v) ≤ b for every v∈ V and ∑v∈Vh(v)≡0(mod2). A spanning subgraph F of G is called an (a, b)-parity factor, if dF(v) ≡ a≡ b (mod 2) and a≤ dF(v) ≤ b for all v∈ V. In this paper, we have developed sufficient conditions for the existence of all [a, b]-factors and (a, b)-parity factors of G in terms of the independence number and connectivity of G. This work extended an earlier result of Nishimura (J Graph Theory 13: 63–69, 1989). Furthermore, we show that these results are best possible in some cases.
- Subject
- all (a, b)-factors; (a, b)-parity factor; independence number; connectivity
- Identifier
- http://hdl.handle.net/1959.13/1478151
- Identifier
- uon:50117
- Identifier
- ISSN:0126-6705
- Rights
- This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Language
- eng
- Full Text
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