In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring.
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Tree (graph theory)
In mathematics, more specifically graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one simple path. In other words, any connected graph without cycles is a tree. A forest is a disjoint union of trees. The various kinds of data structures referred to as trees in computer science are equivalent to trees in graph theory, although such data structures are commonly rooted trees, and may have additional ordering of branches.
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Almost all
In mathematics, the phrase "almost all" has a number of specialised uses. "Almost all" is sometimes used synonymously with "all but [except except] finitely many" (formally, a cofinite set) or "all but a countable set" (formally, a cocountable set); see almost. A simple example is that almost all prime numbers are odd. (Two is a prime number. ) When speaking about the reals, sometimes it means "all reals but a set of Lebesgue measure zero".
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NP-complete
In computational complexity theory, the complexity class NP-complete (abbreviated NP-C or NPC) is a class of decision problems. A decision problem L is NP-complete if it is in the set of NP problems so that any given solution to the decision problem can be verified in polynomial time, and also in the set of NP-hard problems so that any NP problem can be converted into L by a transformation of the inputs in polynomial time.
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Time complexity
In computer science, the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the size of the input to the problem. The time complexity of an algorithm is commonly expressed using big O notation, which suppresses multiplicative constants and lower order terms. When expressed this way, the time complexity is said to be described asymptotically, i.e. , as the input size goes to infinity.
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Graph (mathematics)
In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics.
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Asymptotic analysis
In mathematical analysis, asymptotic analysis is a method of describing limiting behavior. The methodology has applications across science. Examples are in computer science in the analysis of algorithms, considering the performance of algorithms when applied to very large input datasets. the behavior of physical systems when they are very large. in accident analysis when identifying the causation of crash through count modeling with large number of crash counts in a given time and space.
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Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting ("there are 6 coins on the table") and ordering ("this is the 3rd largest city in the country"). These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively. A later notion is that of a nominal number, which is used only for naming. Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory.
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