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Graphs Obtained from Collections of Blocks
Electronic Journal of Graph Theory and Applications
  • Colton Magnant, Georgia Southern Universtiy
  • Pouria Salehi Nowbandegani, Georgia Southern Universtiy
  • Hua Wang, Georgia Southern University
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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


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Citation Information
Colton Magnant, Pouria Salehi Nowbandegani and Hua Wang. "Graphs Obtained from Collections of Blocks" Electronic Journal of Graph Theory and Applications Vol. 3 Iss. 1 (2015) p. 50 - 55 ISSN: 2338-2287
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