# Questions tagged [colorings]

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### $n^2$-Grid $3n$-Coloring Game: Can we color a n-square grid with 3n colors s. t. we can't select n colors to get an histogram with $\Theta(n^2)$ area?

The coloring game is a game played between Alice and Bob. There exists a grid of size $n \times n$, where $n$ is a strictly positive integer. Each cell of the grid can be colored with a color that ...
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### Where can I find a picture of the complete 9-map on a triple torus that corresponds to Heffter’s table?

What I’m looking for is the analogue of Figure 5 in the paper by Saul Stahl, The Othe Map Coloring Theorem, Mathematics Magazine 1985, which is a complete 8-map $M_8$ on the double torus $S_2$ that ...
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### What number of colorings can guarantee that for every k-element subset there exists a coloring assigns different colors for elements from this subset?

Let $M(n, k)$ be a minimal number $m$ such that there exists set $C$ ($|C|=m$) of colorings of n-element set $[n]$ with $k$ colors such that for every $k$-element subset $K$ of $[n]$ there exists ...
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### Can different knots have the same numbers of quandle colorings for all quandles?

Let $K_1$ and $K_2$ be two knots such that for all finite quandles $X$, the number of colorings of $K_1$ by $X$ is the same as the number of colorings of $K_2$ by $X$. Then my question is, must $K_1$ ...
I would like to find all graphs or lattices which satisfy the following conditions: (1) Graph is bipartite with vertex types $A$ and $B$ ($A$-vertices only connected to $B$-vertices and vice-versa) (...
The Erdős Discrepancy Problem is whether in any two-coloring of the naturals for any $C$ there is a sequence $d, 2d, \ldots nd$ such that the difference of red and blue numbers in it is more than $C$. ...