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A shortest path between two graph vertices (u,v) of a graph (Skiena 1990, p. 225). There may be more than one different shortest paths, all of the same length. Graph ...

A metric on a bunch of segments with a common endpoint O, which defines the distance between two points P_1 and P_2 as the length of the shortest path connecting them inside ...

Consider a horse rider who wishes to feed his horse at a field, gather water from a river, and then return to his tent, all in the smallest overall distance possible. The ...

The height of a tree g is defined as the vertex height of its root vertex, where the vertex height of a vertex v in a tree g is the number of edges on the longest downward ...

The vertex height of a vertex v in a rooted tree is the number of edges on the longest downward path between v and a tree leaf. The height of the root vertex of a rooted tree ...

The Desargues graph is the cubic symmetric graph on 20 vertices and 30 edges illustrated above in several embeddings. It is isomorphic to the generalized Petersen graph ...

A braid is an intertwining of some number of strings attached to top and bottom "bars" such that each string never "turns back up." In other words, the path of each string in ...

Consider the length of the diagonal of a unit square as approximated by piecewise linear steps that may only be taken in the right and up directions. Obviously, the length so ...

A continuous transformation from one function to another. A homotopy between two functions f and g from a space X to a space Y is a continuous map G from X×[0,1]|->Y such ...

A tree with a finite number of branches at each fork and with a finite number of leaves at the end of each branch is called a finitely branching tree. König's lemma states ...