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Graph coloring game. 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.
A graphical game is represented by a graph , in which each player is represented by a node, and there is an edge between two nodes and iff their utility functions are dependent on the strategy which the other player will choose. Each node in has a function , where is the degree of vertex . specifies the utility of player as a function of his ...
The Shannon switching game is a connection game for two players, invented by American mathematician and electrical engineer Claude Shannon, the "father of information theory", some time before 1951. [1] Two players take turns coloring the edges of an arbitrary graph. One player has the goal of connecting two distinguished vertices by a path of ...
v. t. e. Game theory is the study of mathematical models of strategic interactions. [ 1 ] It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. [ 2 ] Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly ...
Pursuit–evasion. Pursuit–evasion (variants of which are referred to as cops and robbers and graph searching) is a family of problems in mathematics and computer science in which one group attempts to track down members of another group in an environment. Early work on problems of this type modeled the environment geometrically. [1]
Let H 1 and H 2 be arbitrary trees (or graphs) that have the same Sprague-Grundy value. Consider the two graphs G 1 = G x : H 1 and G 2 = G x : H 2, where G x : H i represents the graph constructed by attaching the tree H i to the vertex x of the graph G. The colon principle states that the two graphs G1 and G2 have the same Sprague-Grundy ...
1 Examples and types of graphs. 2 Graph coloring. 3 Paths and cycles. 4 Trees. ... Graph coloring game; Graph two-coloring; Harmonious coloring; Incidence coloring ...
The chip-firing game is a one-player game on a graph which was invented around 1983 and since has become an important part of the study of structural combinatorics. Each vertex has the number of "chips" indicated by its state variable. On each firing, a vertex is selected and one of its chips is transferred to each neighbour (vertex it shares ...
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