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An R 2 of 1 indicates that the regression predictions perfectly fit the data. Values of R 2 outside the range 0 to 1 occur when the model fits the data worse than the worst possible least-squares predictor (equivalent to a horizontal hyperplane at a height equal to the mean of the observed data). This occurs when a wrong model was chosen, or ...
We can also generalize the induced Ramsey's theorem to a multicolor setting. For graphs H 1, H 2, …, H r, define r ind (H 1, H 2, …, H r) to be the minimum number of vertices in a graph G such that any coloring of the edges of G into r colors contain an induced subgraph isomorphic to H i where all edges are colored in the i-th color for ...
An undirected graph with three vertices and three edges. In one restricted but very common sense of the term, [1] [2] a graph is an ordered pair = (,) comprising: , a set of vertices (also called nodes or points);
Spectral graph theory is the branch of graph theory that uses spectra to analyze graphs. See also spectral expansion. split 1. A split graph is a graph whose vertices can be partitioned into a clique and an independent set. A related class of graphs, the double split graphs, are used in the proof of the strong perfect graph theorem. 2.
The p-value for the permutation test is the proportion of the r values generated in step (2) that are larger than the Pearson correlation coefficient that was calculated from the original data. Here "larger" can mean either that the value is larger in magnitude, or larger in signed value, depending on whether a two-sided or one-sided test is ...
According to the theorem, there exists a number R k (s) such that, whenever n ≥ R(s), such a coloring is not possible. For instance, R 2 (3) = 6, that is, if the edges of the graph K 6 are 2-colored, there will always be a monochromatic triangle. A path in an edge-colored graph is said to be a rainbow path if no color repeats on it. A graph ...
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each internal vertex are equal to each other. [1]
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 ...