%0 Journal Article %1 orourke2010solid %A O'Rourke, Joseph %D 2010 %J CoRR %K 4ct %T A Note on Solid Coloring of Pure Simplicial Complexes %U http://arxiv.org/abs/1012.4017 %V abs/1012.4017 %X We establish a simple generalization of a known result in the plane. The simplices in any pure simplicial complex in R^d may be colored with d+1 colors so that no two simplices that share a (d-1)-facet have the same color. In R^2 this says that any planar map all of whose faces are triangles may be 3-colored, and in R^3 it says that tetrahedra in a collection may be "solid 4-colored" so that no two glued face-to-face receive the same color.

@article{orourke2010solid, abstract = {We establish a simple generalization of a known result in the plane. The simplices in any pure simplicial complex in R^d may be colored with d+1 colors so that no two simplices that share a (d-1)-facet have the same color. In R^2 this says that any planar map all of whose faces are triangles may be 3-colored, and in R^3 it says that tetrahedra in a collection may be "solid 4-colored" so that no two glued face-to-face receive the same color.}, added-at = {2019-10-19T07:17:04.000+0200}, author = {O'Rourke, Joseph}, biburl = {https://www.bibsonomy.org/bibtex/22321876f1e29d4de21a1c357bf7f2513/witdba}, description = {A Note on Solid Coloring of Pure Simplicial Complexes}, interhash = {99de7f4f94b2beec2003e877ac69d630}, intrahash = {2321876f1e29d4de21a1c357bf7f2513}, journal = {CoRR}, keywords = {4ct}, language = {en}, note = {cite arxiv:1012.4017Comment: 11 pages, 6 figures}, timestamp = {2019-10-19T07:17:04.000+0200}, title = {A Note on Solid Coloring of Pure Simplicial Complexes}, url = {http://arxiv.org/abs/1012.4017}, volume = {abs/1012.4017}, year = 2010 }