Tagged Questions
0
votes
1answer
76 views
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)
1
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3answers
124 views
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 ...
3
votes
0answers
44 views
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 $R(\delta)$ ...
1
vote
1answer
71 views
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 ...
3
votes
3answers
221 views
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 ...
3
votes
1answer
137 views
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 ...
5
votes
3answers
180 views
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 ...
2
votes
1answer
74 views
How to calculate number of lumps of a 1D discrete point distribution?
I would like to calculate the number of lumps of a given set of points.
Defining "number of lumps" as "the number of groups with points at distance 1"
Supose we have a discrete 1D space in this ...
1
vote
0answers
94 views
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 ...
