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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.
Given this formula, Rayo's number is defined as: [5] The smallest number bigger than every finite number with the following property: there is a formula () in the language of first-order set-theory (as presented in the definition of ) with less than a googol symbols and as its only free variable such that: (a) there is a variable assignment ...
Graph pebbling is a mathematical game played on a graph with zero or more pebbles on each of its vertices. 'Game play' is composed of a series of pebbling moves. A pebbling move on a graph consists of choosing a vertex with at least two pebbles, removing two pebbles from it, and adding one to an adjacent vertex (the second removed pebble is discarded from play). π(G), the pebbling number of a ...
Moreover, the clique number ω(G) of a graph G is the number of vertices in a maximum clique in G. The intersection number of G is the smallest number of cliques that together cover all edges of G. The clique cover number of a graph G is the smallest number of cliques of G whose union covers the set of vertices V of the graph.
Whether you use Microsoft Office Excel, Google Sheets or Apple Numbers, there’s a free spreadsheet for you. These budgeting templates will give you a head start from simple monthly and yearly ...
A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a column chart and has been identified as the prototype of charts. [1]
Therefore, the worst-case number of comparisons needed to select the second smallest is + ⌈ ⌉, the same number that would be obtained by holding a single-elimination tournament with a run-off tournament among the values that lost to the smallest value. However, the expected number of comparisons of a randomized selection algorithm can ...
Example graph with the state variables s(v) indicated A possible finite firing sequence, with the vertex to be fired in red – the game ends as each vertex has s smaller than its degree. 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 ...