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A Go endgame begins when the board is divided into areas that are isolated from all other local areas by living stones, such that each local area has a polynomial size canonical game tree. In the language of combinatorial game theory , it happens when a Go game decomposes into a sum of subgames with polynomial size canonical game trees.
Lasker's book Go and Go-moku (1934) helped spread the game throughout the U.S., [97] and in 1935, the American Go Association was formed. Two years later, in 1937, the German Go Association was founded. World War II put a stop to most Go activity, since it was a popular game in Japan, but after the war, Go continued to spread. [98]
The concepts of sente and gote are important in higher level Go strategy. A player whose moves compel the opponent to respond in a local position is said to have sente ( ε ζ ) , meaning the player has the initiative; the opponent is said to have gote ( εΎζ ) .
A connected graph has an Euler cycle if and only if every vertex has an even number of incident edges. The term Eulerian graph has two common meanings in graph theory. One meaning is a graph with an Eulerian circuit, and the other is a graph with every vertex of even degree. These definitions coincide for connected graphs. [2]
Paper and pencil go is a Go variant that can be played with just paper and pencil. [14] Unlike standard Go, games played under these rules are guaranteed to end in a finite number of moves, and no ko rule is needed. Nothing is ever rubbed out. It differs from standard Go in the following ways: Surrounded stones are not captured, but just marked.
A ternary plot, ternary graph, triangle plot, simplex plot, or Gibbs triangle is a barycentric plot on three variables which sum to a constant. [1] It graphically depicts the ratios of the three variables as positions in an equilateral triangle .
A 3-map graph is a planar graph, and every planar graph can be represented as a 3-map graph. Every 4-map graph is a 1-planar graph , a graph that can be drawn with at most one crossing per edge, and every optimal 1-planar graph (a graph formed from a planar quadrangulation by adding two crossing diagonals to every quadrilateral face) is a 4-map ...
In computer science, the Hopcroft–Karp algorithm (sometimes more accurately called the Hopcroft–Karp–Karzanov algorithm) [1] is an algorithm that takes a bipartite graph as input and produces a maximum-cardinality matching as output — a set of as many edges as possible with the property that no two edges share an endpoint.