Fáry
Fáry is a mathematical theorem in graph theory, named after the Hungarian mathematician István Fáry, who first proved it in 1948. The theorem states that every simple planar graph can be embedded in the plane such that its edges are represented by straight line segments, with no crossings. This means that any graph that can be drawn on a plane without edge intersections can be realized with straight-line edges, simplifying the visualization and analysis of planar graphs.
The significance of Fáry's theorem lies in its implications for graph drawing and topological graph theory.
Fáry's proof is constructive, offering a method to transform any planar embedding into a straight-line embedding,
Overall, Fáry's theorem is a fundamental result that bridges combinatorial and geometric aspects of graph theory,