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The Thue number of a graph is the minimum number of colors needed in any nonrepetitive coloring. [ 1 ] Variations on this concept involving vertex colorings or more general walks on a graph have been studied by several authors including Barát and Varjú, Barát and Wood (2005), Brešar and Klavžar (2004), and Kündgen and Pelsmajer.
In the same way, the doubly triangular numbers also count the number of distinct ways of coloring the four corners or the four edges of a square with colors, allowing some colors to be unused and counting two colorings as being the same when they differ from each other only by rotation or reflection of the square. The number of choices of ...
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The square tiling has 9 uniform colorings: 1111, 1112(a), 1112(b), 1122, 1123(a), 1123(b), 1212, 1213, 1234. In geometry, a uniform coloring is a property of a uniform figure (uniform tiling or uniform polyhedron) that is colored to be vertex-transitive.
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The first perfect squared square discovered, a compound one of side 4205 and order 55. [1] Each number denotes the side length of its square. Squaring the square is the problem of tiling an integral square using only other integral squares. (An integral square is a square whose sides have integer length.)
Use these free pumpkin carving patterns and stencils to create the best jack-o-lantern on the block. Choose from spooky, cute, and advanced templates. 60 Cute and Spooky Printable Halloween ...
For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.