Nebeský, Ladislav A characterization of the decay number of a connected graph. (English) Zbl 0854.05089 Math. Slovaca 45, No. 4, 349-352 (1995). 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)]. Cited in 1 Document MSC: 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C35 Extremal problems in graph theory Keywords:decay number; spanning tree; number of components; cotree Citations:Zbl 0760.05032 PDF BibTeX XML Cite \textit{L. Nebeský}, Math. Slovaca 45, No. 4, 349--352 (1995; Zbl 0854.05089) Full Text: EuDML References: [1] BEHZAD M., CHARTRAND G., LESNIAK-FOSTER L.: Graphs & Digraphs. Prindle, Weber & Schmidt, Boston, 1979. · Zbl 0403.05027 [2] NASH-WILLIAMS C. ST. J. A.: Edge-disjoint spanning trees of finite graphs. J. London Math. Soc. 36 (1961), 445-450. · Zbl 0102.38805 [3] ŠKOVIERA M.: The decay number and the maximum genus of a graph. Math. Slovaca 42 (1992), 391-406. · Zbl 0760.05032 [4] TUTTE W. T.: On the problem of decomposing a graph into n connected factors. J. London Math. Soc. 36 (1961), 221-230. · Zbl 0096.38001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.