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r/dataisbeautiful, also known as Data Is Beautiful, is a subreddit dedicated to aesthetically pleasing works of data visualization. [ 2 ] [ 3 ] [ 4 ] It was created in 2012; as of January 2022, it has over 20 million members.
[a] Ramsey's theorem states that there exists a least positive integer R(r, s) for which every blue-red edge colouring of the complete graph on R(r, s) vertices contains a blue clique on r vertices or a red clique on s vertices. (Here R(r, s) signifies an integer that depends on both r and s.) Ramsey's theorem is a foundational result in ...
An example of "beauty in method"—a simple and elegant visual descriptor of the Pythagorean theorem.. Mathematical beauty is the aesthetic pleasure derived from the abstractness, purity, simplicity, depth or orderliness of mathematics.
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.
A random r-regular graph is a graph selected from ,, which denotes the probability space of all r-regular graphs on vertices, where < and is even. [1] It is therefore a particular kind of random graph, but the regularity restriction significantly alters the properties that will hold, since most graphs are not regular.
In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given size. It is one of the central results of extremal graph theory, an area studying the largest or smallest graphs with given properties, and is a special case of the forbidden subgraph problem on the maximum number of edges in a graph that ...
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For every graph G, there exists a highly irregular graph H containing G as an induced subgraph. [3] This last observation can be considered analogous to a result of Dénes Kőnig, which states that if H is a graph with greatest degree r, then there is a graph G which is r-regular and contains H as an induced subgraph. [3]