Questions tagged [colorings]

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5
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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
1answer
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
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0answers
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
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1answer
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
2answers
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
0answers
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
1answer
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 $C$. ...