2016/04/21 by Adan Medrano Martin del Campo, del Campo, Adan Medrano Martin, Sylvain Carpentier +1
Computer Science · Engineering · Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1604.06176
openalex publication_date 2016/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Every graph Γ can be embedded in the plane with a minimal number of edge intersections, called its classical crossing number cross(Γ). In this paper, we prove that if Γ is a metric graph it can be realized as a tropical curve in the plane with exactly cross(Γ) crossings, where the tropical curve is equipped with the lattice length metric. Our result has an application in algebraic geometry, as it enables us to construct a rational map of non-Archimedean curves into the projective plane, whose tropicalization is almost faithful when restricted to their skeleton.