Integral and rational graphs in the plane

DOI10.1007/S00373-024-02841-1MaRDI QIDQ6632146

Jozsef Solymosi

Publication date: 4 November 2024

Published in: Graphs and Combinatorics (Search for Journal in Brave)

zbMATH Keywords

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Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Erd?s problems and related topics of discrete geometry (52C10) General theory of distance geometry (51K05) Infinite graphs (05C63)

Cites Work

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• On rational approximation of a geometric graph
• Definability of Frobenius orbits and a result on rational distance sets
• On a question of Erdős and Ulam
• There are integral heptagons, no three points on a line, no four on a circle
• Every graph is an integral distance graph in the plane
• A solution of the Erdős-Ulam problem on rational distance sets assuming the Bombieri-Lang conjecture
• Odd wheels are not odd-distance graphs
• Research Problems in Discrete Geometry
• Straight line embeddings of cubic planar graphs with integer edge lengths
• Points at rational distance from the vertices of a triangle
• Integral distances
• Integral distances
• The Erdős–Ulam problem, Lang's conjecture and uniformity
• Plane integral drawings of planar graphs

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