What are Bridges of Graphs? | Graph Theory, Edge Deletion

[@sophiabnrm8730]

Your videos on Graph Theory are really special and one of a kind. I am looking constantly for tutorials on this topic but they are very rare - especially in this kind of quality!! I would love to see more graph theory proofs, because its sometimes difficult to come up with the initial idea on how to solve them (at least for me). But any of your videos are greatly appreciated! Wish you all the best!

[@WrathofMath]

Thanks so much for watching and for your kind words! I put hours of work into the lessons everyday to make them as high quality as possible, I'm glad you're finding them helpful! After a recent poll I did it seems most viewers want more Graph Theory, and that's exactly what I've got lined up (among other things)! The proof I mentioned in this lesson (edge is a bridge iff it lies on no cycles) will be out Sunday morning and there are more to come after that! If you didn't already see the previous lesson, it's a classic graph theory proof on Eulerian graphs I recommend checking out! kzbin.info/www/bejne/rXScaodplrt3gbM A lot of graph theory proofs use the strategy of taking an object we know exists that we think will have the property we want, then proving it has that property. For example to prove a graph has a Hamiltonian path, what kind of path will be Hamiltonian? A longest path! So we take a longest path and prove it is Hamiltonian, but taking that longest path is the big starting point! Induction is also often a very reliable way to prove many things that might have other more elegant proofs, but induction is unbelievably effective and as valid a proof as any other! And of course contradiction is a staple of many of the Graph Theory proofs we do as well. Thanks again and wishing you all the best in your graph theory studies! Keep on proving and practicing!

[@PunmasterSTP]

Graph theory, edge deletion? More like "Great videos; thanks for the information!" 👍

[@amoschoo938]

Wow your videos are informative and right to the point. Keep it up the good work.. Was really surprised i had to scroll down so far to find your videos

[@WrathofMath]

Thanks so much for watching and I'm glad it helped! I do what I can to get them to appear near the top of relevant search results, but a lot of it is left up to the algorithm. I'm glad you found it and if you didn't already see the lesson on the bridge-related proof I mentioned in this video, check it out! kzbin.info/www/bejne/ooS3aaCCo95sps0

[@samsunnahar9175]

Thanks a lot for your excellent lecture!!

[@luciano8158]

nice foreshadowing!!

[@PunmasterSTP]

It kept me on the...edge...of my seat!

[@luciano8158]

@@PunmasterSTP yes!

[@PunmasterSTP]

@@luciano8158 It was bridgin' great!