Existence theorems for floorplans

• Main Author: Rinsma, I.
• Language: en
• Published: University of Canterbury. Mathematics 2013
• Online Access: http://hdl.handle.net/10092/8425

The existence of floorplans with given areas and adjacencies for the rooms cannot always be guaranteed. Rectangular, isometric and convex floorplans are considered. For each, the areas of the rooms and a graph representing the required internal adjacencies between the rooms is given. This thesis gives existence theorems for a floorplan satisfying these conditions. If the graph is maximal outerplanar, only a convex floorplan can always be guaranteed. Floorplans of each type can be found if the graph is a tree. A branching index is defined for a tree, and used to give the minimum number of vertices of degree 2 in any maximal outerplanar graph, in which the tree can be embedded. If the graph of adjacencies is a tree, and each room in the plan is external, once again only convex floorplans can always be guaranteed. Rectangular floorplans can always be found in some cases, depending on the embedding index of the tree.