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A k-coloring of a graph G is a vertex coloring that is an assignment of one of k possible colors to each vertex of G (i.e., a vertex coloring) such that no two adjacent ...

A cograph (or "complement-reducible graph") is simple graph defined by the criteria 1. K_1 is a cograph, 2. If X is a cograph, then so is its graph complement, and 3. If X ...

A maximal subgraph of an undirected graph such that any two edges in the subgraph lie on a common simple cycle.

A problem asking for the shortest tour of a graph which visits each edge at least once (Kwan 1962; Skiena 1990, p. 194). For an Eulerian graph, an Eulerian cycle is the ...

A fundamental structural result in extremal graph theory due to Szemerédi (1978). The regularity lemma essentially says that every graph can be well-approximated by the union ...

The clique covering number theta(G) of a graph G is the minimum number of cliques in G needed to cover the vertex set of G. Since theta(G) involves the minimum number of ...

A two-coloring of a complete graph K_n of n nodes which contains exactly the number of monochromatic forced triangles and no more (i.e., a minimum of R+B where R and B are ...

Two nonisomorphic graphs can share the same graph spectrum, i.e., have the same eigenvalues of their adjacency matrices. Such graphs are called cospectral. For example, the ...

An AB percolation is a discrete percolation model in which the underlying point lattice graph L has the properties that each of its graph vertices is occupied by an atom ...

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 ...