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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 ...

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 ...

A (Delta,D)-graph is a graph with maximum vertex degree Delta and diameter at most D. The order of a graph with degree Delta of diameter D is bounded by ...

The chromatic number of a graph G is the smallest number of colors needed to color the vertices of G so that no two adjacent vertices share the same color (Skiena 1990, p. ...