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The following other wikis use this file: Usage on ar.wikipedia.org مثلث متساوي الأضلاع; فضاء ثنائي الأبعاد; Usage on ar.wikisource.org
This is an accepted version of this page This is the latest accepted revision, reviewed on 7 January 2025. Book containing line art, to which the user is intended to add color For other uses, see Coloring Book (disambiguation). Filled-in child's coloring book, Garfield Goose (1953) A coloring book is a type of book containing line art to which people are intended to add color using crayons ...
A 3-coloring of a triangle-free planar graph. In the mathematical field of graph theory, Grötzsch's theorem is the statement that every triangle-free planar graph can be colored with only three colors.
Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]
and that there exist triangle-free graphs that have chromatic numbers proportional to this bound. There have also been several results relating coloring to minimum degree in triangle-free graphs. Andrásfai, Erdős & Sós (1974) proved that any n-vertex triangle-free graph in which each vertex has more than 2n/5 neighbors must be bipartite.
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