# Questions tagged [colorings]

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7
questions

**5**

votes

**0**answers

261 views

### What do the circuits of this matroid look like?

Given any hypergraph $H=(V,E)$ we call a family of sets $I\subseteq E$ "indifferent" iff there exists a map $\phi:I\to V$ such that: $\forall X\in I(\phi(X)\in X)$ and $\forall X,Y\in I(X\...

**0**

votes

**1**answer

117 views

### maximum number of colors for an optimal tiling which guaranties infinite paths

This question is a more applicable version of the question I've asked in mathexchange recently:
What is the maximum number of colors we can use to color $N^2$ square sub-tiles of $N×N$ square
block ...

**2**

votes

**0**answers

74 views

### How many ways to cover a N×N chessboard with white and black boxes by some restrictions?

Suppose we have a N×N chessboard and the boxes ■, □.
We should cover the chessboard with those boxes but there can not have the 2×2 square $\scriptstyle{\begin{array}{cc}\square&\square\\
\...

**3**

votes

**1**answer

93 views

### 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 ...

**4**

votes

**2**answers

195 views

### 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 $K_1$ ...

**4**

votes

**0**answers

49 views

### Bipartite graphs with alternating edge colorings

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)
(...

**2**

votes

**1**answer

273 views

### Homogeneous van der Waerden

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 $C$.
...