Support the production of this course by joining Wrath of Math as a Channel Member for exclusive and early videos, original music, and upcoming lecture notes for the graph theory series! Plus your comments will be highlighted for me so it is more likely I'll answer your questions! ru-vid.com/show-UCyEKvaxi8mt9FMc62MHcliwjoin Graph Theory course: ru-vid.com/group/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH Graph Theory exercises: ru-vid.com/group/PLztBpqftvzxXtYASoshtU3yEKqEmo1o1L
also this is a great video. your fans certainly appreciate you taking the time to clear up the same confusion i had about the previous video. though given that i have an introductory background with pure math, i was able to make sense of it before this video started, and yes i arrived at the same explanation that you give in this video
You definitely deserve my subscribe. This video was quite meticulous and cleared up any confusion one might have from the last go around with this concept. Keep up the great work.
I had the same confusion with your previous video, about being able to technically add more edges, and still having the graph be connected, but of course then the connected subgraph would no longer even be a subgraph of G in the first place, as we have added a new edge. When talking about maximal connectiveness I guess we just have to be careful to only consider the vertices in the original graph G. So thanks for clearing that up, this video was very well explained as usual :) know that you are saving my degree right now Sean🙏🏼👏
So glad this video could help clear it up, thanks Salman! It's definitely one of those description that can cause some confusion. A maximal connected subgraph is a subgraph that is maximally connected among subgraphs, just like a complete bipartite graph is a bipartite graph that is "complete" among bipartite graphs, even though it isn't "complete" by our general definition.
I'll make it simple if a graph G has A, B and C components and also there is a D subgraph of A this D graph is nothing but a part of already existing graph A which means we can add some edges/nodes to the D subgraph and make it graph A which is a component of graph G. So G: A, B, C , D ; A{ D }. Adding edges to make it maximal => D + (some edges) = A therefore D is not a component it's just a subgraph of A. So Number of components of G is 3 not 4.
Precisely! But the additional terms in the definition of component I think are what cause the confusion. It can be easy to get hung up on "maximal connected" and forget the very important "subgraph of G" part! Thanks for watching!
Thanks a lot for watching, glad it helped! Check out my graph theory playlist if you're looking for more! ru-vid.com/group/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
Thanks for watching and good question! That is true for connected graphs, but if a graph is disconnected then it has multiple components, and is as a whole not a component, since components are connected. Here is another of my videos on the topic: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-q6pKCP1W0dk.html