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Preprints, Working Papers, ... Year : 2023

Minor-Universal Graph for Graphs on Surfaces

Abstract

We show that, for every n and every surface Σ, there is a graph U embeddable on Σ with at most cn^2 vertices that contains as minor every graph embeddable on Σ with n vertices. The constant c depends polynomially on the Euler genus of Σ. This generalizes a well-known result for planar graphs due to Robertson, Seymour, and Thomas [Quickly Excluding a Planar Graph. J. Comb. Theory B, 1994] which states that the square grid on 4n^2 vertices contains as minor every planar graph with n vertices.
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Dates and versions

hal-04090935 , version 1 (10-05-2023)

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Cyril Gavoille, Claire Hilaire. Minor-Universal Graph for Graphs on Surfaces. 2023. ⟨hal-04090935⟩

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CNRS TDS-MACS
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