Lyu, Zhenhua Extremal digraphs avoiding an orientation of the diamond. (English) Zbl 1469.05089 Graphs Comb. 37, No. 4, 1373-1383 (2021). Summary: Let \(H\) be the digraph with vertex set \(\{1,2,3,4\}\) and arc set \(\{12,13,14,24,34\}\). In this paper, we determine the maximum size of \(H\)-free digraphs of order \(n\) as well as the extremal digraphs attaining this maximum size when \(n\geq 16\). Cited in 2 Documents MSC: 05C35 Extremal problems in graph theory 05C20 Directed graphs (digraphs), tournaments 05C12 Distance in graphs Keywords:digraph; orientation; Turán problem PDFBibTeX XMLCite \textit{Z. Lyu}, Graphs Comb. 37, No. 4, 1373--1383 (2021; Zbl 1469.05089) Full Text: DOI References: [1] Brown, WG; Erdős, P.; Simonovits, M., Extremal problems for directed graphs, J. Combin. Theory Ser. B, 15, 77-93 (1973) · Zbl 0253.05124 [2] W.G. Brown, P. Erdős, M. Simonovits, Inverse extremal digraph problems, Finite and infinite sets, Vol. I, II (Eger, 1981), 119-156, Colloq. Math. Soc. János Bolyai, 37, North-Holland, Amsterdam, 1984 · Zbl 0569.05023 [3] W.G. Brown and F. Harary, Extremal digraphs, Combinatorial theory and its applications, I (Proc. Colloq., Balatonfred, 1969), pp. 135-198. North-Holland, Amsterdam, 1970 [4] W.G. Brown, M. Simonovits, Extremal multigraph and digraph problems, Paul Erdős and his mathematics, II (Budapest, 1999), 157-203, Bolyai Soc. Math. Stud., 11, János Bolyai Math. Soc., Budapest, 2002 · Zbl 1029.05080 [5] Huang, Z.; Lyu, Z., 0-1 matrices with zero trace whose squares are 0-1 matrices, Linear Algebra Appl., 565, 156-176 (2019) · Zbl 1410.15058 [6] Huang, Z.; Lyu, Z., Extremal digraphs avoiding an orientation of \(C_4\), Discrete Math., 343, 111827 (2020) · Zbl 1435.05093 [7] Huang, Z.; Lyu, Z., 0-1 matrices whose \(k\)-th powers have bounded entries, Linear Multilinear Algebra, 68, 1972-1982 (2020) · Zbl 1455.15008 [8] Huang, Z.; Lyu, Z.; Qiao, P., A Turán problem on digraphs avoiding distinct walks of a given length with the same endpoints, Discrete Math., 342, 1703-1717 (2019) · Zbl 1414.05133 [9] Huang, Z.; Zhan, X., Digraphs that have at most one walk of a given length with the same endpoints, Discrete Math., 311, 70-79 (2011) · Zbl 1225.05115 [10] Lyu, Z., Digraphs that contain atmost t distinct walks of a given length with the same endpoints, J. Comb. Opt., 41, 762-779 (2021) · Zbl 1464.05162 [11] Z. Lyu, Extremal digraphs avoiding distinct walks of length 4 with the same endpoints. Discuss. Math. Graph T. doi:10.7151/dmgt.2321 · Zbl 1464.05162 [12] P. Turán , Eine Extremalaufgabe aus der Graphentheorie. (Hungarian) Mat. Fiz. Lapok 48 (1941) 436-452 · JFM 67.0732.03 [13] Turán, P., On the theory of graphs, Colloq. Math., 3, 19-30 (1954) · Zbl 0055.17004 [14] D.B. West, Introduction to Graph Theory, Prentice Hall, Inc., 1996 · Zbl 0845.05001 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.