Sufficient conditions for the existence of path-factors with given properties
A spanning subgraph H of a graph G is called a [Formula: see text]-factor of G if every component of H is isomorphic to a path of order at least k, where [Formula: see text] is an integer. A graph G is called a [Formula: see text]-factor-critical graph if [Formula: see text] contains a [Formula: see...
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Taylor & Francis Group
2025-01-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2024.2418640 |
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| author | Hui Qin Guowei Dai Yuan Chen Ting Jin Yuan Yuan |
| author_facet | Hui Qin Guowei Dai Yuan Chen Ting Jin Yuan Yuan |
| author_sort | Hui Qin |
| collection | DOAJ |
| description | A spanning subgraph H of a graph G is called a [Formula: see text]-factor of G if every component of H is isomorphic to a path of order at least k, where [Formula: see text] is an integer. A graph G is called a [Formula: see text]-factor-critical graph if [Formula: see text] contains a [Formula: see text]-factor for any [Formula: see text] with [Formula: see text]. A graph G is called a [Formula: see text]-factor-deleted graph if [Formula: see text] has a [Formula: see text]-factor for any [Formula: see text] with [Formula: see text]. Intuitively, if a graph is dense enough, it will have a [Formula: see text]-factor. In this paper, we give some sufficient conditions for a graph to be a [Formula: see text]-factor-critical graph or a [Formula: see text]-factor-deleted graph. In this paper, we demonstrate that (i) G is a [Formula: see text]-factor-critical graph if its sun toughness [Formula: see text] and [Formula: see text]. (ii) G is a [Formula: see text]-factor-critical graph if its degree sum [Formula: see text] and [Formula: see text]. (iii) G is a [Formula: see text]-factor-deleted graph if its sun toughness [Formula: see text] and [Formula: see text]. (iv) G is a [Formula: see text]-factor-deleted graph if its degree sum [Formula: see text] and [Formula: see text]. |
| format | Article |
| id | doaj-art-607fe2d94b5745eb963c75d7d010b915 |
| institution | Kabale University |
| issn | 0972-8600 2543-3474 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj-art-607fe2d94b5745eb963c75d7d010b9152025-02-03T13:29:42ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742025-01-011610.1080/09728600.2024.2418640Sufficient conditions for the existence of path-factors with given propertiesHui Qin0Guowei Dai1Yuan Chen2Ting Jin3Yuan Yuan4School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, P.R. ChinaSchool of Mathematical Science & Institute of Mathematics, Nanjing Normal University, Nanjing, P.R. ChinaResearch Center of Nonlinear Science, School of Mathematical and Physical Sciences, Wuhan Textile University, Wuhan, P.R. ChinaCollege of Science, Nanjing Forestry University, Nanjing, P.R. ChinaSchool of Science, Hainan University, Haikou, P.R. ChinaA spanning subgraph H of a graph G is called a [Formula: see text]-factor of G if every component of H is isomorphic to a path of order at least k, where [Formula: see text] is an integer. A graph G is called a [Formula: see text]-factor-critical graph if [Formula: see text] contains a [Formula: see text]-factor for any [Formula: see text] with [Formula: see text]. A graph G is called a [Formula: see text]-factor-deleted graph if [Formula: see text] has a [Formula: see text]-factor for any [Formula: see text] with [Formula: see text]. Intuitively, if a graph is dense enough, it will have a [Formula: see text]-factor. In this paper, we give some sufficient conditions for a graph to be a [Formula: see text]-factor-critical graph or a [Formula: see text]-factor-deleted graph. In this paper, we demonstrate that (i) G is a [Formula: see text]-factor-critical graph if its sun toughness [Formula: see text] and [Formula: see text]. (ii) G is a [Formula: see text]-factor-critical graph if its degree sum [Formula: see text] and [Formula: see text]. (iii) G is a [Formula: see text]-factor-deleted graph if its sun toughness [Formula: see text] and [Formula: see text]. (iv) G is a [Formula: see text]-factor-deleted graph if its degree sum [Formula: see text] and [Formula: see text].https://www.tandfonline.com/doi/10.1080/09728600.2024.2418640path-factorsun toughnessdegree sum-factor-critical graph-factor-deleted graph05C38 |
| spellingShingle | Hui Qin Guowei Dai Yuan Chen Ting Jin Yuan Yuan Sufficient conditions for the existence of path-factors with given properties AKCE International Journal of Graphs and Combinatorics path-factor sun toughness degree sum -factor-critical graph -factor-deleted graph 05C38 |
| title | Sufficient conditions for the existence of path-factors with given properties |
| title_full | Sufficient conditions for the existence of path-factors with given properties |
| title_fullStr | Sufficient conditions for the existence of path-factors with given properties |
| title_full_unstemmed | Sufficient conditions for the existence of path-factors with given properties |
| title_short | Sufficient conditions for the existence of path-factors with given properties |
| title_sort | sufficient conditions for the existence of path factors with given properties |
| topic | path-factor sun toughness degree sum -factor-critical graph -factor-deleted graph 05C38 |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2024.2418640 |
| work_keys_str_mv | AT huiqin sufficientconditionsfortheexistenceofpathfactorswithgivenproperties AT guoweidai sufficientconditionsfortheexistenceofpathfactorswithgivenproperties AT yuanchen sufficientconditionsfortheexistenceofpathfactorswithgivenproperties AT tingjin sufficientconditionsfortheexistenceofpathfactorswithgivenproperties AT yuanyuan sufficientconditionsfortheexistenceofpathfactorswithgivenproperties |