# Coloring rectangular blocks in 3-space

Colton Magnant; Daniel M. Martin

Discussiones Mathematicae Graph Theory (2011)

- Volume: 31, Issue: 1, page 161-170
- ISSN: 2083-5892

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topColton Magnant, and Daniel M. Martin. "Coloring rectangular blocks in 3-space." Discussiones Mathematicae Graph Theory 31.1 (2011): 161-170. <http://eudml.org/doc/271037>.

@article{ColtonMagnant2011,

abstract = {If rooms in an office building are allowed to be any rectangular solid, how many colors does it take to paint any configuration of rooms so that no two rooms sharing a wall or ceiling/floor get the same color? In this work, we provide a new construction which shows this number can be arbitrarily large.},

author = {Colton Magnant, Daniel M. Martin},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {chromatic number; channel assignment problem; 3 dimensional rectangular blocks; 3-dimensional rectangular blocks},

language = {eng},

number = {1},

pages = {161-170},

title = {Coloring rectangular blocks in 3-space},

url = {http://eudml.org/doc/271037},

volume = {31},

year = {2011},

}

TY - JOUR

AU - Colton Magnant

AU - Daniel M. Martin

TI - Coloring rectangular blocks in 3-space

JO - Discussiones Mathematicae Graph Theory

PY - 2011

VL - 31

IS - 1

SP - 161

EP - 170

AB - If rooms in an office building are allowed to be any rectangular solid, how many colors does it take to paint any configuration of rooms so that no two rooms sharing a wall or ceiling/floor get the same color? In this work, we provide a new construction which shows this number can be arbitrarily large.

LA - eng

KW - chromatic number; channel assignment problem; 3 dimensional rectangular blocks; 3-dimensional rectangular blocks

UR - http://eudml.org/doc/271037

ER -

## References

top- [1] J.P. Burling, On coloring problems of families of prototypes, Ph.D. Thesis - University of Colorado, 1, (1965)
- [2] T.R. Jensen and B. Toft, Graph coloring problems, Wiley-Interscience Series in Discrete Mathematics and Optimization (John Wiley & Sons Inc., New York, 1995). A Wiley-Interscience Publication.
- [3] A.V. Kostochka and J. Nesetril, Properties of Descartes' construction of triangle-free graphs with high chromatic number, Combin. Probab. Comput. 8 (1999) 467-472, doi: 10.1017/S0963548399004022. Zbl0951.05036
- [4] B. Reed and D. Allwright, Painting the office, MICS Journal 1 (2008) 1-8.

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