Abstract
Let (Formula presented.) be a set of graphs. A graph (Formula presented.) is said to be (Formula presented.) -free if (Formula presented.) does not contain (Formula presented.) as an induced subgraph for all (Formula presented.) in (Formula presented.), and we call (Formula presented.) a forbidden pair if (Formula presented.). In 2008, Faudree et al. characterized all pairs of connected graphs (Formula presented.) such that every 2-connected (Formula presented.) -free graph of sufficiently large order has a 2-factor. In 2013, Fujisawa et al. characterized all pairs of connected graphs (Formula presented.) such that every connected (Formula presented.) -free graph of sufficiently large order with minimum degree at least two has a 2-factor. In this paper, we generalize these two results by considering disconnected graphs (Formula presented.). In other words, we characterize all pairs of graphs (Formula presented.) such that every 2-connected (Formula presented.) -free graph of sufficiently large order has a 2-factor. We also characterize all pairs of graphs (Formula presented.) such that every connected (Formula presented.) -free graph of sufficiently large order with minimum degree at least two has a 2-factor.
| Original language | English |
|---|---|
| Pages (from-to) | 209-231 |
| Number of pages | 23 |
| Journal | Journal of Graph Theory |
| Volume | 100 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jun 2022 |
Keywords
- 2-factor
- closure
- disconnected graph
- forbidden subgraph