Geodesic
A note on extremal results on directed acyclic graphs
Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 445-454.

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This paper studies the maximum number of edges of a Directed Acyclic Graph (DAG) with n vertices in terms of it’s longest path ℓ. We prove that in general this number is the Turán number t(n, l + 1), the maximum number of edges in a graph with n vertices without a clique of size ℓ + 2. Furthermore, we find the maximum number of edges in a DAG which is either reduced, strongly reduced or extremely reduced and we relate this extremal result with the family of intersection graphs of families of boxes with transverse intersection.
DOI : 10.26493/1855-3974.1107.1c8
Keywords: Directed graphs, Turán numbers, intersection graphs of families of boxes 
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Álvaro Martínez-Pérez; Luis Montejano; Deborah Oliveros. A note on extremal results on directed acyclic graphs. Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 445-454. doi : 10.26493/1855-3974.1107.1c8. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1107.1c8/

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