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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.
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 ...
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 ...
An example of a chart containing gratuitous chartjunk. This chart uses a large area and much "ink" (many symbols and lines) to show only five hard-to-read numbers, 1, 2, 4, 8, and 16. Chartjunk consists of all visual elements in charts and graphs that are not necessary to comprehend the information represented on the graph, or that distract the ...
A similar game with larger numbers of cops can be used to define the cop number of a graph, the smallest number of cops needed to win the game. The cop-win graphs are exactly the graphs of cop number equal to one. [22] Bonato and Nowakowski describe this game intuitively as the number of ghosts that would be needed to force a Pac-Man player to ...
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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 ...