1. Minimum degree of minimal (n-10)-factor-critical graphs.
- Author
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Guo, Jing and Zhang, Heping
- Subjects
- *
INTEGERS , *LOGICAL prediction - Abstract
A graph G of order n is said to be k -factor-critical for integers 1 ≤ k < n , if the removal of any k vertices results in a graph with a perfect matching. A k -factor-critical graph G is called minimal if for any edge e ∈ E (G) , G − e is not k -factor-critical. In 1998, O. Favaron and M. Shi conjectured that every minimal k -factor-critical graph of order n has minimum degree k + 1 and confirmed it for k = 1 , n − 2 , n − 4 and n − 6. By using a novel approach, we have confirmed it for k = n − 8 in a previous paper. Continuing with this method, we confirm the conjecture when k = n − 10 in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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