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Vertex coloring is often used to introduce graph coloring problems, since other coloring problems can be transformed into a vertex coloring instance. For example, an edge coloring of a graph is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring ...
The graph coloring game is a mathematical game related to graph theory. Coloring game problems arose as game-theoretic versions of well-known graph coloring problems. In a coloring game, two players use a given set of colors to construct a coloring of a graph, following specific rules depending on the game we consider. One player tries to ...
The present tense (abbreviated PRES or PRS) is a grammatical tense whose principal function is to locate a situation or event in the present time. [1] The present tense is used for actions which are happening now. In order to explain and understand present tense, it is useful to imagine time as a line on which the past tense, the present and ...
The simple present is the most commonly used verb form in English, accounting for more than half of verbs in spoken English. [1] It is called "simple" because its basic form consists of a single word (like write or writes), in contrast with other present tense forms such as the present progressive (is writing) and present perfect (has written).
The name line graph comes from a paper by Harary & Norman (1960) although both Whitney (1932) and Krausz (1943) used the construction before this. [1] Other terms used for the line graph include the covering graph, the derivative, the edge-to-vertex dual, the conjugate, the representative graph, and the θ-obrazom, [1] as well as the edge graph ...
Line chart showing the population of the town of Pushkin, Saint Petersburg from 1800 to 2010, measured at various intervals. A line chart or line graph, also known as curve chart, [1] is a type of chart that displays information as a series of data points called 'markers' connected by straight line segments. [2]
Therefore, a planar graph is simple if and only if its dual has no 1- or 2-edge cutsets; that is, if it is 3-edge-connected. The simple planar graphs whose duals are simple are exactly the 3-edge-connected simple planar graphs. [10] This class of graphs includes, but is not the same as, the class of 3-vertex-connected simple planar graphs. For ...
A directed graph with three vertices and four directed edges (the double arrow represents an edge in each direction). 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:
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