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  2. Grötzsch graph - Wikipedia

    en.wikipedia.org/wiki/Grötzsch_graph

    In the mathematical field of graph theory, the Grötzsch graph is a triangle-free graph with 11 vertices, 20 edges, chromatic number 4, and crossing number 5. It is named after German mathematician Herbert Grötzsch , who used it as an example in connection with his 1959 theorem that planar triangle-free graphs are 3-colorable.

  3. Triangle-free graph - Wikipedia

    en.wikipedia.org/wiki/Triangle-free_graph

    An independent set of ⌊ ⌋ vertices (where ⌊ ⌋ is the floor function) in an n-vertex triangle-free graph is easy to find: either there is a vertex with at least ⌊ ⌋ neighbors (in which case those neighbors are an independent set) or all vertices have strictly less than ⌊ ⌋ neighbors (in which case any maximal independent set must have at least ⌊ ⌋ vertices). [4]

  4. Complete bipartite graph - Wikipedia

    en.wikipedia.org/wiki/Complete_bipartite_graph

    A complete bipartite graph of K 4,7 showing that Turán's brick factory problem with 4 storage sites (yellow spots) and 7 kilns (blue spots) requires 18 crossings (red dots) For any k, K 1,k is called a star. [2] All complete bipartite graphs which are trees are stars. The graph K 1,3 is called a claw, and is used to define the claw-free graphs ...

  5. Graph theory - Wikipedia

    en.wikipedia.org/wiki/Graph_theory

    A directed graph or digraph is a graph in which edges have orientations. In one restricted but very common sense of the term, [5] a directed graph is an ordered pair = (,) comprising: , a set of vertices (also called nodes or points);

  6. Worksheet - Wikipedia

    en.wikipedia.org/wiki/Worksheet

    The form comes with two worksheets, one to calculate exemptions, and another to calculate the effects of other income (second job, spouse's job). The bottom number in each worksheet is used to fill out two if the lines in the main W4 form. The main form is filed with the employer, and the worksheets are discarded or held by the employee.

  7. Glossary of graph theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_graph_theory

    The H-free graphs are the family of all graphs (or, often, all finite graphs) that are H-free. [10] For instance the triangle-free graphs are the graphs that do not have a triangle graph as a subgraph. The property of being H-free is always hereditary. A graph is H-minor-free if it does not have a minor isomorphic to H. Hadwiger 1. Hugo Hadwiger 2.