# Tagged Questions

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### Proof for the length of the shortest 4-connected path and 8-connected path on a chessboard

I have a chessboard with a square marked with A as in the following figure: $$\begin{array}{|c|c|c|} \hline 8&1&2\\ \hline 7&A&3\\ \hline 6&5&4\\ \hline \end{array}$$ The ...
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### Weights for degree ordering

Let $x_1,x_2,x_3$ be indeterminates. Fix an integer $k\geq 3$. Consider the set $M$ of all monomials of the form $x_1^{i_1}.x_2^{i_2}.x_3^{i_3}$ where each $i_j\in \mathbb{N}$ with $i_j\geq 1$ and ...
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### example that shows that the edge chromatic number may be larger than the maximal degree

What is an example that shows that the edge chromatic number may be larger than the maximal degree ∆ ≤ X’(G)
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### Proving by induction that an equilateral triangle will always be divided into (n+1)^2 small triangles?

I'm working on a proof that looks like this: Let $n$ be a positive integer. Given an equilateral triangle, place $n$ points on each side, dividing the side into $n+1$ equal segments. Use the ...
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### Upper bounds on rate of q-ary codes

Among the many upper bounds for families of codes in $\mathbb F _2 ^n$, the best known bound is the one by McEliece, Rodemich, Rumsey and Welch (MRRW) which states that the rate $R(\delta)$ ...
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### Unit Distance Problem Formulated as Point-Circle Incidence Problem

The unit distance problem in the plane asks for the maximum number $U(n)$ of unit distances which can be obtained by $n$ points. For $k$ unit circles and $m$ points in the plane, $I(k,m)$ counts the ...
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### Help me name or find the existing name for this geometric concept!

This may have a proper name, if so - let's discuss. If not, let's name it. This is for a web application in C#, so whatever we call it I will start naming as such in my code. I'm taking GPS data as a ...
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### crossing number question

Prove that there exists constant k such that, for all $5v < e$ there is a subgraph of the complete graph of $v$ vertics with crossing number less or equal than $k e^3/v^2$. Any hints for a way to ...
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### Number of point subsets that can be covered by a disk

Given $n$ distinct points in the (real) plane, how many distinct non-empty subsets of these points can be covered by some (closed) disk? I conjecture that if no three points are collinear and no four ...
### Complexity of Counting the number of inducing $n$-gons
Definition: A $n$-gon is simple if it has no self intersection and is in general position if no pair of its edges are parallel. It is clear that by extending the edges of each simple $n$-gon in ...