# Colouring polytopic partitions in ${\mathbb{R}}^{d}$

Mathematica Bohemica (2002)

- Volume: 127, Issue: 2, page 251-264
- ISSN: 0862-7959

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topKřížek, Michal. "Colouring polytopic partitions in $\mathbb {R}^d$." Mathematica Bohemica 127.2 (2002): 251-264. <http://eudml.org/doc/249039>.

@article{Křížek2002,

abstract = {We consider face-to-face partitions of bounded polytopes into convex polytopes in $\mathbb \{R\}^d$ for arbitrary $d\ge 1$ and examine their colourability. In particular, we prove that the chromatic number of any simplicial partition does not exceed $d+1$. Partitions of polyhedra in $\mathbb \{R\}^3$ into pentahedra and hexahedra are $5$- and $6$-colourable, respectively. We show that the above numbers are attainable, i.e., in general, they cannot be reduced.},

author = {Křížek, Michal},

journal = {Mathematica Bohemica},

keywords = {colouring multidimensional maps; four colour theorem; chromatic number; tetrahedralization; convex polytopes; finite element methods; domain decomposition methods; parallel programming; combinatorial geometry; six colour conjecture; colouring multidimensional maps; four colour theorem; chromatic number; tetrahedralization; convex polytopes; finite element methods; domain decomposition methods; parallel programming; combinatorial geometry; six colour conjecture},

language = {eng},

number = {2},

pages = {251-264},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Colouring polytopic partitions in $\mathbb \{R\}^d$},

url = {http://eudml.org/doc/249039},

volume = {127},

year = {2002},

}

TY - JOUR

AU - Křížek, Michal

TI - Colouring polytopic partitions in $\mathbb {R}^d$

JO - Mathematica Bohemica

PY - 2002

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 127

IS - 2

SP - 251

EP - 264

AB - We consider face-to-face partitions of bounded polytopes into convex polytopes in $\mathbb {R}^d$ for arbitrary $d\ge 1$ and examine their colourability. In particular, we prove that the chromatic number of any simplicial partition does not exceed $d+1$. Partitions of polyhedra in $\mathbb {R}^3$ into pentahedra and hexahedra are $5$- and $6$-colourable, respectively. We show that the above numbers are attainable, i.e., in general, they cannot be reduced.

LA - eng

KW - colouring multidimensional maps; four colour theorem; chromatic number; tetrahedralization; convex polytopes; finite element methods; domain decomposition methods; parallel programming; combinatorial geometry; six colour conjecture; colouring multidimensional maps; four colour theorem; chromatic number; tetrahedralization; convex polytopes; finite element methods; domain decomposition methods; parallel programming; combinatorial geometry; six colour conjecture

UR - http://eudml.org/doc/249039

ER -

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