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Intersection Number (graph Theory)
In the mathematical field of graph theory, the intersection number of a graph G=(V,E) is the smallest number of elements in a representation of G as an intersection graph of finite sets. In such a representation, each vertex is represented as a set, and two vertices are connected by an edge whenever their sets have a common element. Equivalently, the intersection number is the smallest number of cliques needed to cover all of the edges of G. A set of cliques that cover all edges of a graph is called a clique edge cover or edge clique cover, or even just a clique cover, although the last term is ambiguous: a clique cover can also be a set of cliques that cover all vertices of a graph. Sometimes "covering" is used in place of "cover". As well as being called the intersection number, the minimum number of these cliques has been called the ''R''-content, edge clique cover number, or clique cover number. The problem of computing the intersection number has been called the intersect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Faber–Lovász Conjecture
In graph theory, the Erdős–Faber–Lovász conjecture is a problem about graph coloring, named after Paul Erdős, Vance Faber, and László Lovász, who formulated it in 1972.. It says: :If complete graphs, each having exactly vertices, have the property that every pair of complete graphs has at most one shared vertex, then the union of the graphs can be properly colored with colors. The conjecture for all sufficiently large values of was proved by Dong Yeap Kang, Tom Kelly, Daniela Kühn, Abhishek Methuku, and Deryk Osthus. Equivalent formulations introduced the problem with a story about seating assignment in committees: suppose that, in a university department, there are committees, each consisting of faculty members, and that all committees meet in the same room, which has chairs. Suppose also that at most one person belongs to the intersection of any two committees. Is it possible to assign the committee members to chairs in such a way that each member si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bitwise And
In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor. Most bitwise operations are presented as two-operand instructions where the result replaces one of the input operands. On simple low-cost processors, typically, bitwise operations are substantially faster than division, several times faster than multiplication, and sometimes significantly faster than addition. While modern processors usually perform addition and multiplication just as fast as bitwise operations due to their longer instruction pipelines and other architectural design choices, bitwise operations do commonly use less power because of the reduced use of resources. Bitwise operators In the explanations below, any indication of a bit's position is counted from the right (least sig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Food Web
A food web is the natural interconnection of food chains and a graphical representation of what-eats-what in an ecological community. Position in the food web, or trophic level, is used in ecology to broadly classify organisms as autotrophs or heterotrophs. This is a non-binary classification; some organisms (such as carnivorous plants) occupy the role of mixotrophs, or autotrophs that additionally obtain organic matter from non-atmospheric sources. The linkages in a food web illustrate the feeding pathways, such as where heterotrophs obtain organic matter by feeding on autotrophs and other heterotrophs. The food web is a simplified illustration of the various methods of feeding that link an ecosystem into a unified system of exchange. There are different kinds of consumer–resource interactions that can be roughly divided into herbivory, carnivory, scavenging, and parasitism. Some of the organic matter eaten by heterotrophs, such as sugars, provides energy. Autotrophs and hetero ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compact Letter Display
Compact Letter Display (CLD) is a statistical method to clarify the output of multiple hypothesis testing when using the Analysis of variance, ANOVA and Tukey's range test, Tukey's range tests. CLD can also be applied following the Duncan's new multiple range test (which is similar to Tukey's range test). CLD facilitates the identification of variables, or Factor analysis, factors, that have Statistical difference testing, statistically different means (or averages) vs. the ones that do not have statistically different means (or averages). The basic technique of compact letter display is to label variables by one or more letters, so that variables are statistically indistinguishable if and only if they share at least one letter. The problem of doing so, using as few distinct letters as possible can be represented combinatorially as the problem of computing an Intersection number (graph theory), edge clique cover of a graph representing pairs of indistinguishable variables. As we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
