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Given a map with genus g>0, Heawood showed in 1890 that the maximum number N_u of colors necessary to color a map (the chromatic number) on an unbounded surface is N_u = ...

Given a square complex or real matrix A, a matrix norm ||A|| is a nonnegative number associated with A having the properties 1. ||A||>0 when A!=0 and ||A||=0 iff A=0, 2. ...

Let G be a graph with A and B two disjoint n-tuples of graph vertices. Then either G contains n pairwise disjoint AB-paths, each connecting a point of A and a point of B, or ...

The Meringer graph is one of the four (5,5)-cage graphs, discovered by Meringer (1999) after it had long been thought that only three such cages existed. Like the other ...

A minimum edge cover is an edge cover having the smallest possible number of edges for a given graph. The size of a minimum edge cover of a graph is known as the edge cover ...

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 ...

A number b_(2n) having generating function sum_(n=0)^(infty)b_(2n)x^(2n) = 1/2ln((e^(x/2)-e^(-x/2))/(1/2x)) (1) = 1/2ln2+1/(48)x^2-1/(5760)x^4+1/(362880)x^6-.... (2) For n=1, ...

The word modulus has several different meanings in mathematics with respect to complex numbers, congruences, elliptic integrals, quadratic invariants, sets, etc. The modulus ...

A polygonal number of the form N_n=n(7n-5)/2, also called an enneagonal number. The first few are 1, 9, 24, 46, 75, 111, 154, 204, ... (OEIS A001106). The generating function ...

Consider the number of sequences that can be formed from permutations of a set of elements such that each partial sum is nonnegative. The number of sequences with nonnegative ...