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.


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