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Based on a problem in particle physics, Dyson (1962abc) conjectured that the constant term in the Laurent series product_(1<=i!=j<=n)(1-(x_i)/(x_j))^(a_i) is the multinomial ...

The Earth-Moon problem is a special case of the empire problem for countries with m=2 disjoint regions, with one region of each country lying on the Earth and one on the Moon ...

In a graph G, contraction of an edge e with endpoints u,v is the replacement of u and v with a single vertex such that edges incident to the new vertex are the edges other ...

The edge count of a graph g, commonly denoted M(g) or E(g) and sometimes also called the edge number, is the number of edges in g. In other words, it is the cardinality of ...

The size of a minimum edge cover in a graph G is known as the edge cover number of G, denoted rho(G). If a graph G has no isolated points, then nu(G)+rho(G)=|G|, where nu(G) ...

The Egawa graph with parameters (p,s) is a distance-regular but not distance-transitive graph on 16^p4^s nodes. These graphs generalize the Doob graphs and give (s,4)-Hamming ...

A graph G with m edges is said to be elegant if the vertices of G can be labeled with distinct integers (0,1,2,...,m) in such a way that the set of values on the edges ...

The empire problem, also known as the m-pire problem) asks for the maximum number of colors needed to color countries such that no two countries sharing a common border have ...

In geometry, an endpoint is one of the two points at the boundary of a line segment. In analysis, an endpoint is one of the two points at the boundary of a closed interval or ...

Erdős and Heilbronn (Erdős and Graham 1980) posed the problem of estimating from below the number of sums a+b where a in A and b in B range over given sets A,B subset= Z/pZ ...