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Binding numbers of fractional \(k\)-deleted graphs. (English) Zbl 1219.05141

Summary: Let \(k\) be an integer with \(k \geq 2\). We show that if \(G\) be a graph such that \(|G| > 4k+1 -4\sqrt {k-1}\) and \(\text{bind}(G)> \frac{(2k-1)(n-1)}{k(n-2)},\) then \(G\) is a fractional \(k\)-deleted graph. We also show that in the case where \(k\) is even, if \(G\) be a graph such that \(|G| > 4k+1 -4\sqrt {k}\) and \(\text{bind}(G)> \frac{(2k-1)(n-1)}{k(n-2)+1},\) then \(G\) is a fractional \(k\)-deleted graph.

MSC:

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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References:

[1] Y. Egawa and H. Enomoto, Sufficient conditions for the existence of k -factors, Recent studies in graph theory (1989), 96-105, Vishwa, Gulbarga.
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[3] D. R. Woodall, The binding number of a graph and its Anderson number, J. Combinatorial Theory Ser. B 15 (1973), 225-255. · Zbl 0253.05139 · doi:10.1016/0095-8956(73)90038-5
[4] S. Zhou, A result on fractional k -deleted graphs. (Preprint). · Zbl 1183.05068
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