Novikov, B. V.; Polyakova, L. Yu.; Zholtkevich, G. N. Decomposition of directed graphs and the Turán problem. (English) Zbl 1308.05091 Ukr. Math. J. 66, No. 7, 1070-1084 (2014) and Ukr. Mat. Zh. 66, No. 7, 958-969 (2014). Summary: We consider vertex decompositions of (di)graphs appearing in the automata theory and establish some properties of these decompositions. These decompositions are applied to the problem of forbidden subgraphs. MSC: 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C20 Directed graphs (digraphs), tournaments 05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 65C20 Probabilistic models, generic numerical methods in probability and statistics 68Q45 Formal languages and automata Keywords:vertex decompositions of digraphs; forbidden subgraphs PDFBibTeX XMLCite \textit{B. V. Novikov} et al., Ukr. Math. J. 66, No. 7, 1070--1084 (2014; Zbl 1308.05091) Full Text: DOI arXiv References: [1] M. Dokuchaev, B. Novikov, and G. Zholtkevych, “Partial actions and automata,” Alg. Discrete Math., 11, No. 2, 51-63 (2011). · Zbl 1255.68098 [2] A.V. Aho and J. D. Ullman, The Theory of Parsing, Translation, and Compiling. Vol. 2. Compiling, Prentice-Hall (1973). · Zbl 0309.68068 [3] B. Bollobas, “Modern graph theory,” Grad. Texts Math., 184 (1998). · Zbl 0902.05016 [4] D. B. West, Introduction to Graph Theory, Pearson Education (2001). [5] P. Turán, “On an extremal problem in graph theory (in Hungarian),” Mat. Fiz. Lapok, 46, 436-452 (1941). [6] E. M. Eschen, Ch. T. Hoang, J. P. Spinrad, and R. Sritharan, “On graphs without a <Emphasis Type=”Italic“>C4 or a diamond,” Discrete Appl. Math., 159, No. 7, 581-587 (2011). · Zbl 1213.05244 · doi:10.1016/j.dam.2010.04.015 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.