In this video we discuss the problem of finding a tight upper bound on the number of edges a graph on n vertices can have if it is also known that the graph has no 3-cycle in it. This is known as Mantel's Theorem and it is a special case of Turan's Theorem which generalizes this problem from a 3-cycle (a complete graph on 3 vertices) to complete graphs on arbitrary numbers of vertices. #TuranGraph #MantelsTheorem #GraphTheory CHECK OUT OTHER TYPES OF VIDEOS: ================================ GRE Math Subject Test: https://www.youtube.com/playlist?list=PLBiVnG9A5gceFbk7oTBHALETI2SUmplIL Putnam Math Competition: https://www.youtube.com/playlist?list=PLBiVnG9A5gcdLg0Im3qewDrgcMxpbjcqN Math Theorem Corner: https://www.youtube.com/playlist?list=PLBiVnG9A5gccu9O8aCjVsynisfQLQyGOe Math Problems Corner: https://www.youtube.com/playlist?list=PLBiVnG9A5gcc_1Kzd2xkHMXdO8zHz-W_4 Math Insights: https://www.youtube.com/playlist?list=PLBiVnG9A5gcfHRbtZcfQdJuUMAS6v48uj Academic Advice: https://www.youtube.com/playlist?list=PLBiVnG9A5gce-PPdJQmtPNMsivAKKuXwe GET MY BOOK ON AMAZON!! ======================== "Number Theory Towards RSA Cryptography in 10 Undergraduate Lectures" https://www.amazon.com/Number-Theory-Toward-Cryptography-Undergraduate/dp/1978457464 CHECK ME OUT ON THE INTERNET!! ============================== Website: www.mohamedomar.org Twitter: @ProfOmarMath Instagram: profomarmath YouTube: www.youtube.com/ProfOmarMath And of course, subscribe to my channel!