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seen May 30 '13 at 12:11

May
30
comment Can any planar graph have 4 vertices and 4 regions?
Actually I am confused at that point because the book (Grimaldi, Discrete and Combinatorial Mathematics) I read considers the region outside as infinite region and takes it into account.
May
30
comment Can any planar graph have 4 vertices and 4 regions?
@kyticka in short yes, here you can read en.wikipedia.org/wiki/Planar_graph
May
30
comment Can any planar graph have 4 vertices and 4 regions?
See the second image from top. I'm considering this represenation. rip94550.wordpress.com/2008/11/30/…
May
30
revised Given $G = (V,E)$, a planar, connected graph with cycles, Prove: $|E| \leq \frac{s}{s-2}(|V|-2)$. $s$ is the length of smallest cycle
added 426 characters in body
May
30
comment Given $G = (V,E)$, a planar, connected graph with cycles, Prove: $|E| \leq \frac{s}{s-2}(|V|-2)$. $s$ is the length of smallest cycle
Ok, so observe that $2e \geq sr$, $r$ is region in your notation it is $f$, face.
May
30
answered Given $G = (V,E)$, a planar, connected graph with cycles, Prove: $|E| \leq \frac{s}{s-2}(|V|-2)$. $s$ is the length of smallest cycle
May
30
asked Can any planar graph have 4 vertices and 4 regions?
Jan
13
awarded  Commentator
Jan
5
comment How many elements of order d?
@DonAntonio thank you for your feedback! Can you mention me the way you thought to find the answer, I'm interested in different solution
Jan
5
comment How do I find this limit?
@BabakSorouh the 2 answers below are actually what I meant, seems like working
Jan
5
comment How do I find this limit?
you can start with taking the ln of limit
Jan
5
asked How many elements of order d?
Jan
2
awarded  Enthusiast
Dec
21
awarded  Supporter
Dec
21
awarded  Student
Dec
21
asked How to evaluate $\int_0^{2\pi} \frac{d\theta}{A+B\cos\theta}$?
Dec
21
comment How do I find the number of group homomorphisms from $S_3$ to $\mathbb{Z}/6\mathbb{Z}$?
can it be possible that the trivial one should not be taken into account, otherwise I dont see any explanation, I'm quite what I've explained.
Dec
18
answered How do I find the number of group homomorphisms from $S_3$ to $\mathbb{Z}/6\mathbb{Z}$?
Dec
6
answered On Ceva's Theorem?
Dec
6
revised Decomposing a subgroup
I've needed to first prove this on my own before sharing.