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A connected bipartite graph is called Hamilton-laceable, a term apparently introduced in Simmons (1978), if it has a u-v Hamiltonian path for all pairs of vertices u and v, ...

A perfect matching of a graph is a matching (i.e., an independent edge set) in which every vertex of the graph is incident to exactly one edge of the matching. A perfect ...

A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...

Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees (valencies) of its graph vertices. The number of degree sequences for ...

A function f is said to be an entire modular form of weight k if it satisfies 1. f is analytic in the upper half-plane H, 2. f((atau+b)/(ctau+d))=(ctau+d)^kf(tau) whenever [a ...

Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these ...

A coordinate chart is a way of expressing the points of a small neighborhood, usually on a manifold M, as coordinates in Euclidean space. An example from geography is the ...

A family gamma of nonempty subsets of X whose union contains the given set X (and which contains no duplicated subsets) is called a cover (or covering) of X. For example, ...

Let A_1, A_2, A_3, and A_4 be four points on a circle, and H_1, H_2, H_3, H_4 the orthocenters of triangles DeltaA_2A_3A_4, etc. If, from the eight points, four with ...

An edge cover is a subset of edges defined similarly to the vertex cover (Skiena 1990, p. 219), namely a collection of graph edges such that the union of edge endpoints ...