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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.
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
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
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 …