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A parsimonious coloring, for a given graph and vertex ordering, has been defined to be a coloring produced by a greedy algorithm that colors the vertices in the given order, and only introduces a new color when all previous colors are adjacent to the given vertex, but can choose which color to use (instead of always choosing the smallest) when ...
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). [1]
McKinney made the pandas project public in 2009. [6] McKinney left AQR in 2010 to start a PhD in Statistics at Duke University. He went on leave from Duke in the summer of 2011 to devote more time to developing Pandas, [6] culminating in the writing of Python for Data Analysis in 2012. In 2012, he co-founded Lambda Foundry Inc. [7]
The smallest number of colors needed to color a graph G is called its chromatic number, and is often denoted χ(G). Sometimes γ(G) is used, since χ(G) is also used to denote the Euler characteristic of a graph. A graph that can be assigned a (proper) k-coloring is k-colorable, and it is k-chromatic if its chromatic number is exactly k.
The choosability (or list colorability or list chromatic number) ch(G) of a graph G is the least number k such that G is k-choosable. More generally, for a function f assigning a positive integer f ( v ) to each vertex v , a graph G is f -choosable (or f -list-colorable ) if it has a list coloring no matter how one assigns a list of f ( v ...
Apply a bipartite graph edge coloring algorithm to H. Each color class in H corresponds to a set of edges in G that form a subgraph with maximum degree two; that is, a disjoint union of paths and cycles, so for each color class in H it is possible to form three color classes in G.
Lambda calculus consists of constructing lambda terms and performing reduction operations on them. A term is defined as any valid lambda calculus expression. In the simplest form of lambda calculus, terms are built using only the following rules: [a]: A variable is a character or string representing a parameter. (.
Given an n × n square matrix A of real or complex numbers, an eigenvalue λ and its associated generalized eigenvector v are a pair obeying the relation [1] =,where v is a nonzero n × 1 column vector, I is the n × n identity matrix, k is a positive integer, and both λ and v are allowed to be complex even when A is real.l When k = 1, the vector is called simply an eigenvector, and the pair ...