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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
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References:

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