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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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2025-01-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2024.2418640 |
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| Summary: | 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]. |
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| ISSN: | 0972-8600 2543-3474 |