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The complex plane is the plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number. Every complex number corresponds to a unique point in the ...

Chvátal defines the term hole to mean "a chordless cycle of length at least four." The restriction "of length at least four" allows use of the term "hole" regardless of if ...

Consider an n×n (0, 1)-matrix such as [a_(11) a_(23) ; a_(22) a_(34); a_(21) a_(33) ; a_(32) a_(44); a_(31) a_(43) ; a_(42) a_(54); a_(41) a_(53) ; a_(52) a_(64)] (1) for ...

A minimum vertex cover is a vertex cover having the smallest possible number of vertices for a given graph. The size of a minimum vertex cover of a graph G is known as the ...

P. G. Tait undertook a study of knots in response to Kelvin's conjecture that the atoms were composed of knotted vortex tubes of ether (Thomson 1869). He categorized knots in ...

A graph is planar if it can be drawn in a plane without graph edges crossing (i.e., it has graph crossing number 0). The number of planar graphs with n=1, 2, ... nodes are 1, ...

A permutation, also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. The ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

The Pierce expansion, or alternated Egyptian product, of a real number 0<x<1 is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

A (-1,0,1)-matrix is a matrix whose elements consist only of the numbers -1, 0, or 1. The number of distinct (-1,0,1)-n×n matrices (counting row and column permutations, the ...