topological graph theory

mathematics

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July 17, 2026

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Topological graph theory is a subfield of mathematics that combines concepts from graph theory and topology. Graph theory studies networks of points (vertices) connected by lines (edges). Topology, often called "rubber sheet geometry," examines properties of objects that remain unchanged under continuous deformations like bending or stretching, without tearing or gluing.12

In topological graph theory, a key focus is on planar graphs—graphs that can be drawn on a plane without edges crossing except at vertices. This field explores how graphs can be embedded on different surfaces and relates to problems like map coloring. It also investigates concepts such as Eulerian circuits and Hamiltonian circuits, which are paths that traverse edges or vertices in specific ways.1

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graph theory
…led to a subfield called topological graph theory. An important problem in this area concerns planar graphs. These are graphs that can be drawn as dot-and-line diagrams on a plane (or, equivalently, on a sphere) without any edges crossing except at the vertices where they meet. Complete graphs with four…
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…led to a subfield called topological graph theory. An important problem in this area concerns planar graphs. These are graphs that can be drawn as dot-and-line diagrams on a plane (or, equivalently, on a sphere) without any edges crossing except at the vertices where they meet. Complete graphs with four…
Read More