Tuza, Zsolt Perfect graph decompositions. (English) Zbl 0768.05058 Graphs Comb. 7, No. 1, 89-93 (1991). Proved are three theorems presenting upper and lower bounds of the minimum number of perfect subgraphs covering or partitioning either the vertex set or the edge set Wolfram MathWorld of a given graph. The weighted versions of both cases are studied, too. All the theorems are based on four lemmas, one of which being proved and published by the author in 1986. Reviewer: V.O.Groppen (Vladikaukaz) MSC: 05C35 Extremal problems in graph theory 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) Keywords:decompositions; bound; weight; bounds; covering; partitioning × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Erdös, P.: Some remarks on the theory of graphs. Bull. Amer. Math. Soc.53, 292–294 (1947) · Zbl 0032.19203 · doi:10.1090/S0002-9904-1947-08785-1 [2] Erdös, P., Szekeres, G.: A combinatorial problem in geometry. Compos. Math.2, 463–470 (1935) · Zbl 0012.27010 [3] Lovász, L.: A characterization of perfect graphs. J. Comb. Theory Ser. B13, 95–98 (1972) · Zbl 0241.05107 · doi:10.1016/0095-8956(72)90045-7 [4] Tuza, Zs.: Intersection properties and extremal problems for set systems. In: Irregularities of Partitions (G. Halász and V.T. Sós, Eds.), Proc. Colloq. Math. Soc. János Bolyai, Fertöd (Hungary) 1986, Springer-Verlag, 1989, pp. 141–151 · Zbl 0719.05068 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.