Unit Rectangle Visibility Graphs
Abstract
Over the past twenty years, rectangle visibility graphs have generated considerable interest, in part due to their applicability to VLSI chip design. Here we study unit rectangle visibility graphs, with fixed dimension restrictions more closely modeling the constrained dimensions of gates and other circuit components in computer chip applications. A graph $G$ is a unit rectangle visibility graph (URVG) if its vertices can be represented by closed unit squares in the plane with sides parallel to the axes and pairwise disjoint interiors, in such a way that two vertices are adjacent if and only if there is a nondegenerate horizontal or vertical band of visibility joining the two rectangles. Our results include necessary and sufficient conditions for $K_n$, $K_{m,n}$, and trees to be URVGs, as well as a number of general edge bounds.
 Publication:

arXiv eprints
 Pub Date:
 October 2007
 arXiv:
 arXiv:0710.2279
 Bibcode:
 2007arXiv0710.2279D
 Keywords:

 Mathematics  Combinatorics;
 05C62 (Primary);
 05C10 (Secondary)
 EPrint:
 27 Pages, 25 figures