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seen Sep 17 at 20:12

Jul
19
comment Vertex transitive and edge transitive and line graph
$G=K_3+K_{1,3}$ is a counterexample. The line-graph of $G$ is vertex transitive but $G$ is not edge transitive.
Jul
18
awarded  Civic Duty
Jul
12
awarded  Critic
Jun
23
revised Estimate for the travelling salesman problem for balls inside a grid
added 83 characters in body
Jun
23
revised Estimate for the travelling salesman problem for balls inside a grid
added 83 characters in body
Jun
23
answered Estimate for the travelling salesman problem for balls inside a grid
Jun
23
comment Estimate for the travelling salesman problem for balls inside a grid
I see... so then it might be a good idea to edit the question and replace "path" by "walk", as a "path" in a graph usually means that it visits no vertex more than once.
Jun
20
comment Estimate for the travelling salesman problem for balls inside a grid
Regarding question 2), which paths do you consider? What is a "path", actually, by your definition?
Jun
20
comment Estimate for the travelling salesman problem for balls inside a grid
So, by "ball", you mean the ball in the $\ell_1$-norm, that is, a square with sides of angles $\pi/4$ with respect to the axes?
Jun
19
answered Angle of a regular simplex
Jun
17
answered A bound on a set
Jun
17
comment A bound on a set
@Joybangla As GH from MO correctly noticed, I misread the question and assumed that $\alpha_i \in \{-1,1\}$.
Jun
16
comment A bound on a set
Yes, Sperner Theorem gives the upper bound ${n \choose \lfloor n/2\rfloor}$. For $\alpha>2$, one can use the generalization to families of subsets with no chains of length $r$, where $r=\lceil\alpha/2\rceil+1$. See en.wikipedia.org/wiki/Sperner%27s_theorem#No_long_chains
Jun
13
comment Hiding $k$ disks inside a larger disk
And for four discs, there are a continuum many configurations where the integral is $\pi +4$.
Jun
12
comment Hiding $k$ disks inside a larger disk
Now for two such touching discs, the integral is $\pi + 2$, and for three discs like on the picture the integral is $\pi + 3$. Asymptotically, and approximately, it seems you want to pack the discs into another disc of smallest diameter (and thus perimeter).
Jun
11
answered Hiding $k$ disks inside a larger disk
May
29
awarded  Yearling
May
20
revised Wait time to grid network disconnection with failing edges
now considering also separators formed by two noncontractible curves
May
20
comment Wait time to grid network disconnection with failing edges
You are absolutely right, I missed those disconnected disconnectors; they should be included in the calculations. Fortunately, we have to consider only pairs of boundary curves. Since we are on the torus, at least one of the components of every disconnected subgraph has at most two boundary components (either one contractible curve of a pair of parallel noncontractible curves).
May
19
revised Wait time to grid network disconnection with failing edges
added the second sentence, corrected the upper bound