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The harmonic conjugate to a given function u(x,y) is a function v(x,y) such that f(x,y)=u(x,y)+iv(x,y) is complex differentiable (i.e., satisfies the Cauchy-Riemann ...

Let L be a lattice (or a bounded lattice or a complemented lattice, etc.), and let C_L be the covering relation of L: C_L={(x,y) in L^2|x covers y or y covers x}. Then C_L is ...

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 ...

A Meyniel graph, also called a very strongly perfect graph, is a graph in which every odd cycle of length five or more has at least two chords. Meyniel graphs are perfect. ...

An outerplanar graph is a graph that can be embedded in the plane such that all vertices lie on the outer face. Outerplanar graphs are planar and, by their definition, ...

A plane figure or solid compound consisting of multiple connected copies of a given base shape. For example, affixing n equal squares gives an n-polyomino, while affixing n ...

A topological transformation in which a surface is made out of an infinitely elastic material which, however, may not be torn or cut. Using this simple prescription gives the ...

A scale-free network is a connected graph or network with the property that the number of links k originating from a given node exhibits a power law distribution ...

A connected graph having e graph edges is said to be sequential if it is possible to label the nodes i with distinct integers f_i in {0,1,2,...,e-1} such that when graph edge ...

Let A be an edge cut of a connected graph G. Then the cyclic edge connectivity lambda_c(G) is the size of a smallest cyclic edge cut, i.e., a smallest edge cut A such that ...