A graph G=(V,E) is given. If at least n colors are required to paints its vertices so that between any two same colored vertices no edge is connected, then call this graph ''n-colored''. Prove that for any n∈ℕ, there is a n-colored graph without triangles.

Hi guys,

I'm Paolo and this is the second round of the second edition of Oliforum contest. You can see first round here.

I copy below all rules, as always

1- The contest is made of 2 rounds, this is the last one.

2- Each round is made of some problems (from 3 to 5..), and i will give points 0 to 7: 6 for all correct solutions, 7 for only elegants and correct solutions (similar to ML contest).

3- It is tought for high-school student, and also for undergraduate or higher student, but you cannot use non-elementary-theory, otherwise the solution is invalid.

4- All begins from italian-oliforum and the classification is unique.

5- The first round starts on 15:00 of 16 september and it ends on 15:00 of 18 seprember, so you have 48 hours .
NB. All times (date and hours) are according to ROME MERIDIAN (+2GTM), please attention!

6- Enrollment is not necessary, it sufficies to send me solution.

7- Time of arriving solution is not important.

8- Way of sending solutions.
- You need to send solutions to both email address: pao_leo88 ML hotmail ML it and leonettipaolo ML gmail ML com in a unique pdf file (so, with attachment) of a right size;
- The pdf file must be written with Latex (or a way that I can understand);
- You rename the pdf file as your nickname (the same of yours in ML);
- You need to write nothing in the email;
- Try to be clear in solutions!

{If (and only if) you are not able to create a pdf in latex model, you can send me a email in .doc format with solutions, as latex or in a way that i (and all correctors) can understand, or also with private message to me}.

Later, together with texts, I'll make a list below this topic where i'll write all names of who sent me solutions in right way.

For all doubts and questions, ask me in private messages



Thanks for the attentions and good luck

Paolo Leonetti

Check out the Oliforum contest:

Hi guys,

here's the topic of the "Oliforum contest", the competition for training that i'm arranging from some weeks Smile .
i'll try to sumarize all details about it, be carefully.

1- The contest is made of 2 rounds.

2- Each round is made of some problems (from 3 to 5..), and i will give points 0 to 7: 6 for all correct solutions, 7 for only elegants and correct solutions (similar to ML contest).

3- It is tought for high-school student, and also for undergraduate or higher student, but you cannot use non-elementary-theory, otherwise the solution is invalid.

4- All begins from italian-oliforum and the classification is unique.

5- The first round starts on 17:00 of 28 september and it ends on 17:00 of 30 seprember, so you have 48 hours Smile .
NB. All times (date and hours) are according to ROME MERIDIAN (+2GTM), please attention!

6- Enrollment is not necessary, it sufficies to send me solution.

7- Time of arriving solution is not important.

8- Way of sending solutions.
- You need to send solutions to both email address: pao_leo88 ML hotmail ML it and leonettipaolo ML gmail ML com in a unique pdf file (so, with attachment) of a right size; (" ML " needs to be replaced by either @ or .)
- The pdf file must be written with Latex (or a way that I can understand);
- You rename the pdf file as your nickname (the same of yours in ML);
- You need to write nothing in the email;
- Try to be clear in solutions!

{If (and only if) you are not able to create a pdf in latex model, you can send me a email in .doc format with solutions, as latex or in a way that i (and all correctors) can understand, or also with private message to me}.

Later, together with texts, I'll make a list below this topic where i'll write all names of who sent me solutions in right way.

For all doubts and questions, ask me in private messages Wink



Thanks for the attentions and good luck

Paolo Leonetti

There's a new online math competition coming up: Shaastra Online Math Competition, , apparently created by two MathLinkers: madness and Chapplikka.

See more details at http://www.mathlinks.ro/viewtopic.php?t=298135

The official results for the International Mathematical Olympiad (IMO) 2009 in Bremen, Germany can be found here.