Abstract
A directed graph G ∈ 𝒟 is said to be embeddable into G′ ∈ 𝒟 if there exists an injective graph homomorphism φ : G → G′. We consider the embeddability ordering (𝒟, ≤) of finite directed graphs, and prove that for every G ∈ 𝒟 the set {G, G T} is definable by first-order formulas in the partially ordered set (𝒟, ≤), where G T denotes the transpose of G. We also prove that the automorphism group of (𝒟, ≤) is isomorphic to ℤ2.
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This research was realized in the frames of TÁMOP 4.2.4. A/2-11-1-2012-0001 “National Excellence Program—Elaborating and operating an inland student and researcher personal support system” The project was subsidized by the European Union and co-financed by the European Social Fund.
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Kunos, Á. Definability in the Embeddability Ordering of Finite Directed Graphs. Order 32, 117–133 (2015). https://doi.org/10.1007/s11083-014-9319-7
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DOI: https://doi.org/10.1007/s11083-014-9319-7