Timeline for What is the chromatic number of the graph whose vertices dimension $n-2$ subsimplicies of $\Delta^n$ and an edge between two vertices is given if the two associated $n-2$ vertices are contained in the same $n-1$ subsimplex?

7 events

when toggle format	what		by	license	comment
Jan 31, 2012 at 4:16	vote	accept	Spice the Bird
Jan 30, 2012 at 0:40	answer	added	Richard Stanley		timeline score: 5
Jan 30, 2012 at 0:29	history	edited	Spice the Bird	CC BY-SA 3.0	deleted 2 characters in body
Jan 30, 2012 at 0:28	comment	added	Spice the Bird		Woops, I should have said n-colorable. I guess I forgot how to count. As for the first paragraph, that was sort of my motivation for the question. In more informal terms, I want to be able to take an injection, $\delta^{n-1}\hookrightarrow\Delta^n$ that respects the combinatorial structure and extend to all of the boundary, such that any restriction to a face looks like the original map. I am not sure if this helps. I will think about the motivation a bit and edit acordingly.
Jan 30, 2012 at 0:08	comment	added	S. Carnahan♦		I am having trouble making sense of your question. The $\hookrightarrow$ symbol implies you are asking for $\tilde{f}$ to be an inclusion, but you are asking for the restriction to any two faces to coincide, up to permutation of the vertices. This appears to yield a contradiction. Also, the graph for the case $n=2$ appears to be 3-colorable, and that contradicts your experimental results.
Jan 29, 2012 at 23:09	history	edited	Spice the Bird	CC BY-SA 3.0	grammer edit; edited title
Jan 29, 2012 at 23:02	history	asked	Spice the Bird	CC BY-SA 3.0