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The (m,n)-lollipop graph is the graph obtained by joining a complete graph K_m to a path graph P_n with a bridge. Precomputed properties of lollipop graphs are available in ...

There are several regular mathematics competitions available to students. The International Mathematical Olympiad is perhaps the largest, while the William Lowell Putnam ...

A maximally nonhamiltonian graph is a nonhamiltonian graph G for which G+e is Hamiltonian for each edge e in the graph complement of G^_, i.e., every two nonadjacent vertices ...

A two-dimensional grid graph, also known as a rectangular grid graph or two-dimensional lattice graph (e.g., Acharya and Gill 1981), is an m×n lattice graph that is the graph ...

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 nonhamiltonian graph is a graph that is not Hamiltonian. All disconnected graphs are therefore nonhamiltoinian, as are acylic graphs. Classes of connected graphs that are ...

A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...

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 ...

A topological space X is pathwise-connected iff for every two points x,y in X, there is a continuous function f from [0,1] to X such that f(0)=x and f(1)=y. Roughly speaking, ...