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The transitive closure of a binary relation R on a set X is the minimal transitive relation R^' on X that contains R. Thus aR^'b for any elements a and b of X provided that ...

An analog of the polyominoes and polyiamonds in which collections of regular hexagons are arranged with adjacent sides. They are also called hexes, hexas, or polyfrobs ...

An s-route of a graph G is a sequence of vertices (v_0,v_1,...,v_s) of G such that v_iv_(i+1) in E(G) for i=0, 1, ..., s-1 (where E(G) is the edge set of G) and ...

A generalization of Ramsey theory to mathematical objects in which one would not normally expect structure to be found. For example, there exists a graph with very few ...

The fractional edge chromatic number of a graph G is the fractional analog of the edge chromatic number, denoted chi_f^'(G) by Scheinerman and Ullman (2011). It can be ...

A member of a collection of sets is said to be maximal if it cannot be expanded to another member by addition of any element. Maximal sets are important in graph theory since ...

Given a collection of sets, a member set that is not a proper subset of another member set is called a minimal set. Minimal sets are important in graph theory, since many ...

The chromatic polynomial pi_G(z) of an undirected graph G, also denoted C(G;z) (Biggs 1973, p. 106) and P(G,x) (Godsil and Royle 2001, p. 358), is a polynomial which encodes ...

Any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal grid (i.e., the honeycomb, illustrated above). Pappus refers to the ...

The pathwidth of a graph G, also called the interval thickness, vertex separation number, and node searching number, is one less than the size of the largest set in a path ...