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Several prizes are awarded periodically for outstanding mathematical achievement. There is no Nobel Prize in mathematics, and the most prestigious mathematical award is known ...

A simple graph with n>=3 graph vertices in which each graph vertex has vertex degree >=n/2 has a Hamiltonian cycle.

A graph cycle.

For every p, the kernel of partial_p:C_p->C_(p-1) is called the group of cycles, Z_p={c in C_p:partial(c)=0}. (1) The letter Z is short for the German word for cycle, ...

A unicyclic graph is a connected graph containing exactly one cycle (Harary 1994, p. 41). A connected unicyclic graph is therefore a pseudotree that is not a tree. ...

A Hamiltonian path, also called a Hamilton path, is a graph path between two vertices of a graph that visits each vertex exactly once. If a Hamiltonian path exists whose ...

A graph G is said to be locally X, where X is a graph (or class of graphs), when for every vertex v, the graph induced on G by the set of adjacent vertices of V (sometimes ...

There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The ...

The order-n dipole graph D_n is a multigraph consisting of two vertices and n multiple edges joining them. The dipole graph D_2 is a multigraph that can be considered to ...

An elegant algorithm for constructing an Eulerian cycle (Skiena 1990, p. 193).