Title

On Coloring Box Graphs

Status

Faculty

School

School of Science

Department

Math/Computer Science

Document Type

Article

Publication Date

2-6-2015

Publication Title

Discrete Mathematics

Description/Abstract

We consider the chromatic number of a family of graphs we call box graphs, which arise from a box complex in n-space. It is straightforward to show that any box graph in the plane has an admissible coloring with three colors, and that any box graph in n-space has an admissible coloring with n+1 colors. We show that for box graphs in n-space, if the lengths of the boxes in the corresponding box complex take on no more than two values from the set {1,2,3}, then the box graph is 3-colorable, and for some graphs three colors are required. We also show that box graphs in 3-space which do not have cycles of length four (which we call “string complexes”) are 3-colorable.

Keywords

Graph coloring, Box graph, Chromatic number

SMC Affiliated Work

1

Volume

338

Issue

2

First Page

209

Last Page

216

Scholarly

yes

DOI

10.1016/j.disc.2014.09.004

Disciplines

Mathematics

Original Citation

Ellen Veomett (Mathematics and Computer Science):“On Coloring Box Graphs,” by E. Hogan, J. O’Rourke, C. Traub, and E. Veomett, in Discrete Mathematics, Vol 338, Issue 2 (2015), p 209-216. doi:10.1016/j.disc.2014.09.004

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