A graph is a collection of vertices and edges. Vertices are the dots and edges are the lines that connect the dots. On the left, all edges can be redrawn (curved lines are allowed and moving vertices is allowed) such that no edges cross each other and each vertex is still connected to the same other vertices. These graphs are called planar.

A graph is a collection of vertices and edges. Vertices are the dots and edges are the lines that connect the dots. On the left, all edges can be redrawn (curved lines are allowed) such that no edges cross each other and each vertex is still connected to the same other vertices. These graphs are called planar.

A graph is a collection of vertices and edges. Vertices are the dots and edges are the lines that connect the dots. On the left, all edges can be redrawn (curved lines are allowed) such that not edges cross each other and each vertex is still connected to the same other vertices. These graphs are called planar.

Graph can be redrawn such that no edges intersect vs. not so.

A graph is a collection of vertices and edges. Vertices are the dots and edges are the lines that connect the dots. On the left, all edges can be redrawn (curved lines are allowed) such that each vertex is still connected to the same other vertices. These graphs are called planar.

A graph is a collection of vertices and edges. Vertices are the dots and edges are the lines that connect the dots. On the left, all edges can be uncrossed while still holding the integrity of the graph, so they are all planar. On the right, not all edges can be uncrossed, so they are non-planar.

keywords: solved, +null, math, notso

concepts: graph theory, topological transformation(?), vertex of meeting lines(?), planar, crossing

A graph is a collection of vertices and edges. Vertices are the dots and edges are the lines that connect the dots. On the left, all edges can be uncrossed, so they are all planar. On the right, not all edges can be uncrossed, so they are non-planar.

keywords: solved, +null, math, notso

concepts: graph theory, topological transformation(?), vertex of meeting lines(?), planar, crossing

planar vs non-planar

A graph is a collection of vertices and edges. Vertices are the dots and edges are the lines that connect the dots. On the left, all edges can be uncrossed, so they are all planar. On the right, not all edges can be uncrossed, so they are non-planar.

Richard J. Trudeau, Introduction to Graph Theory, Dover Publications, 1976.

Molly C Klenzak

Bongard Problems with "world" small equilateral triangles, circles, and squares all the same size: some filled in black, some outlines vs. other Bongard Problems.

Aaron David Fairbanks