Gridline graphs: a review in two dimensions and an extension to higher dimensions
Gridline graphs can be realized in the plane with vertices adjacent whenever they are on a common vertical or horizontal line. We review some applications and characterizations, e.g. they are line graphs of bipartite graphs, and provide practical O(|V|3) algorithms for some classical problems. We extend gridline graphs from the plane to higher dimensions. We characterize these graphs using a vertex coloring of the clique graph that corresponds to the conditions that, in the intersection graph of lines parallel to axes in , any cycle of four lines must remain in two dimensions and any path between two given lines must traverse the same two dimensions.
gridline graph clique graph graph of a (01)-matrix adjacency graph checked graph line graph of a bipartite graph perfect graph