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Results tagged with graph-colorings
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user 20595
Vertex colouring, Edge Colouring, List Colouring, Fractional Chromatic Number and other variants of graph colouring problems are all on topic.
32
votes
Generalizations of the four-color theorem
The coloring of higher dimensional ball packings.
A ball packing is a collection of balls with disjoint interiors. The tangency graph of a ball packing takes the balls as vertices and connect two v …
11
votes
1
answer
366
views
What is known about the chromatic number for minimum-distance graphs in higher dimensions?
For a set of points in $\mathbb{R}^d$ with minimum distance $a$, the minimum-distance graph connect two points iff they are at distance $a$. We can also view it as the tangency graph for a set of uni …
- 2,581
10
votes
Accepted
Coloring of the plane
Seems to be the polychromatic number of the plane.
According to my knowledge, the value is at least 4 (due to Raiskii) and at most 6 (due to Stechkin).
See Chap. 4 and 6 of The Mathematical Coloring …
- 2,581