Talk:Circular coloring

Example

An example would be very enlightening here, could someone provide one? Stdazi (talk) 20:07, 13 November 2008 (UTC)

See also => Rank coloring

See also => Rank coloring linked to Cycle rank.

Cycle rank does not contain even ONE word color.

So, what is Rank coloring and why this article refer to Cycle rank?

Jumpow (talk) 09:00, 2 February 2019 (UTC)

I've never heard of rank coloring and a Google Scholar search shows that's at best some obscure term from one unavailable paper (Rank Coloring of Graphs by Dereniowski). Other papers are either about comparing the rank of the adjacency matrix to the (usual) chromatic number, a question with no relation to circular coloring; or about cycle rank and the related notion of tree-depth (also known under a dozen other names), but these are also completely unrelated to circular coloring. Tokenzero (talk) 13:45, 2 February 2019 (UTC)

• The inductive definition of cycle rank suggests an assignment of numbers to vertices, i.e. a certain type of vertex coloring (if you suppress the minimum in the definition). The cycle rank is then the minimum number of colors in such a coloring. I've seen somewhere in the literature (on undirected graphs) that the term "coloring" was used for this concept, although they did not use "rank coloring". Maybe the article on tree-depth mentions something in this direction, I haven't checked. Hermel (talk) 23:15, 3 February 2019 (UTC)

Yes, tree-depth is also called centered coloring (basically as you say: one thinks of the numbers as colors) and it's also related to various notions of weak coloring numbers. It's also known as vertex ranking number. But I looked and there's no article mentioning any non-trivial relation between circular coloring and tree-depth, they really have nothing in common except for the fact that both are related to graph homomorphisms. Tokenzero (talk) 23:32, 3 February 2019 (UTC)