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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 ...
Amit Agrawal is an Indian engineer and an institute chair professor at the Department of Mechanical Engineering of the Indian Institute of Technology, Bombay. [1] He leads a group of scientists who are involved in the development of next-generation diagnostic microdevices .
See Families of sets for related families of non-graph combinatorial objects, graphs for individual graphs and graph families parametrized by a small number of numeric parameters, and graph theory for more general information about graph theory. See also Category:Graph operations for graphs distinguished for the specific way of their construction
For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.
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The results for misère play are now conjectured to follow a pattern of length six with some exceptional values: the first player wins in misère Sprouts when the remainder (mod 6) is zero, four, or five, except that the first player wins the one-spot game and loses the four-spot game. The table below shows the pattern, with the two irregular ...
More generally, a matroid is called graphic whenever it is isomorphic to the graphic matroid of a graph, regardless of whether its elements are themselves edges in a graph. [ 2 ] The bases of a graphic matroid M ( G ) {\displaystyle M(G)} are the full spanning forests of G {\displaystyle G} , and the circuits of M ( G ) {\displaystyle M(G)} are ...
This will also apply to any super-graph of K 6. For another proof that there must eventually be a triangle of either color, see the Theorem on friends and strangers. Computer search techniques verified in 1974 that the second player can win Sim with perfect play. [1] A strategy that could be easily implemented by human players was found in 2020 ...