Electronic Journal of Graph Theory and Applications
Given a collection of d-dimensional rectangular solids called blocks, no two of which sharing interior points, construct a block graph by adding a vertex for each block and an edge if the faces of the two corresponding blocks intersect nontrivially. It is known that if d ≥ 3, such block graphs can have arbitrarily large chromatic number. We prove that the chromatic number can be bounded with only a mild restriction on the sizes of the blocks. We also show that block graphs of block configurations arising from partitions of d-dimensional hypercubes into sub-hypercubes are at least d-connected. Bounds on the diameter and the hamiltonicity of such block graphs are also discussed
Magnant, Colton, Pouria Salehi Nowbandegani, Hua Wang.
"Graphs Obtained from Collections of Blocks."
Electronic Journal of Graph Theory and Applications, 3 (1): 50-55.