Abstract
We introduce a closure concept for 2-factors in claw-free graphs that generalizes the closure introduced by the first author. The 2-factor closure of a graph is uniquely determined and the closure operation turns a claw-free graph into the line graph of a graph containing no cycles of length at most 5 and no cycles of length 6 satisfying a certain condition. A graph has a 2-factor if and only if its closure has a 2-factor; however, the closure operation preserves neither the minimum number of components of a 2-factor nor the hamiltonicity or nonhamiltonicity of a graph.
| Original language | English |
|---|---|
| Pages (from-to) | 1573-1579 |
| Number of pages | 7 |
| Journal | Discrete Mathematics |
| Volume | 310 |
| Issue number | 10-11 |
| DOIs | |
| Publication status | Published - 6 Jun 2010 |
Keywords
- 2-factor
- Claw-free graph
- Closure
- Dominating system
- Line graph
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Ryjáček, Z., Xiong, L., & Yoshimoto, K. (2010). Closure concept for 2-factors in claw-free graphs. Discrete Mathematics, 310(10-11), 1573-1579. https://doi.org/10.1016/j.disc.2010.02.004