A characterization of the decay number of a connected graph. (English) Zbl 0854.05089

Summary: We show that the minimum number of components in a cotree of a connected graph \(G\) equals the maximum value of the expression \(2c(G- A)- 1- |A|\), where \(A\) is a set of edges of \(G\) and \(c(G- A)\) denotes the number of components of \(G- A\). This invariant was previously studied in M. Škoviera [ibid. 42, No. 4, 391-406 (1992; Zbl 0760.05032)].


05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C35 Extremal problems in graph theory


Zbl 0760.05032
Full Text: EuDML


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