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The Hungarian algorithm finds a maximum independent edge set on a graph. The algorithm starts with any matching M and constructs a tree via a breadth-first search to find an ...

A tree (also called a bicentral tree) having two nodes that are graph centers. The numbers of bicentered trees on n=1, 2, ... nodes are 0, 1, 0, 1, 1, 3, 4, 11, 20, 51, 108 ...

The blow-up lemma essentially says that regular pairs in Szemerédi's regularity lemma behave like complete bipartite graphs from the point of view of embedding bounded degree ...

Four circles c_1, c_2, c_3, and c_4 are tangent to a fifth circle or a straight line iff T_(12)T_(34)+/-T_(13)T_(42)+/-T_(14)T_(23)=0. (1) where T_(ij) is the length of a ...

Connect-Four is a tic-tac-toe-like two-player game in which players alternately place pieces on a vertical board 7 columns across and 6 rows high. Each player uses pieces of ...

Let three similar isosceles triangles DeltaA^'BC, DeltaAB^'C, and DeltaABC^' be constructed on the sides of a triangle DeltaABC. Then DeltaABC and DeltaA^'B^'C^' are ...

The Miquel configuration is the 6_4 configuration illustrated above. Its Levi graph is the rhombic dodecahedral graph.

A graph vertex in a graph is said to be an odd node if its vertex degree is odd.

A three-colorable graph G is a graph with chromatic number chi(G)<=3.

The 24-cell is a finite regular four-dimensional polytope with Schläfli symbol {3,4,3}. It is also known as the hyperdiamond or icositetrachoron, and is composed of 24 ...