We consider the vertex coloring problem, which may be stated as the problem of minimizing the number of labels that can be assigned to the vertices of a graph G such that each ver...
A d-regular graph has largest or first (adjacency matrix) eigenvalue 1 = d. Consider for an even d 4, a random d-regular graph model formed from d/2 uniform, independent permutat...
Scientists, engineers, and educators commonly need to make graphs that quickly illustrate quantitative ideas yet are not based on specific data sets. We call these graphs quantita...
Three types of geometric structure--grid triangulations, rectangular subdivisions, and orthogonal polyhedra-can each be described combinatorially by a regular labeling: an assignm...
In K(n, n) with edges colored either red or blue, we show that the problem of finding a solution matching, a perfect matching consisting of exactly r red edges, and (n - r) blue e...