The animations and proof are beautiful, but they are presented way too fast. Specifically: 1) You talk too fast. 2) Other than section breaks, there are no pauses to think. 3) You don't leave equations and examples on screen long enough.
I've come to realize this when looking through the videos I've made so far. I will try to slow everything down so it's more digestible, because it seems quite simple to me when I'm making the video (since I have the topic researched), but it is definitely not for anyone else watching.
I'm confused at 7:23. Do you mean G complement doesn't have an independent set with a vertex in each maximum clique? Because by lemma 1 the original G must have one. Edit: I watched with the subtitles and they clearly say G complement and you translate between the two... It is a bit confusing.
At 8:42, I don't see why that has tp be true. If you were to color every vertex from a max independent set with the same color then you would have to color every max independent set a different color, but maybe there could exist a better coloring that doesn't assign the same color to the vertices from the same max independent set.
Let's say that there is some better coloring than the one I described (that uses the independent sets). Since this coloring has less colors, the number of vertices of at least one of its colors will have to be greater than the size of the maximum independent set, which is a contradiction (since it would be a bigger maximum independent set).
I am so glad to have found this gem of a channel
The animations and proof are beautiful, but they are presented way too fast. Specifically:
1) You talk too fast.
2) Other than section breaks, there are no pauses to think.
3) You don't leave equations and examples on screen long enough.
I've come to realize this when looking through the videos I've made so far. I will try to slow everything down so it's more digestible, because it seems quite simple to me when I'm making the video (since I have the topic researched), but it is definitely not for anyone else watching.
Beautifully done!
Lovely stuff 😊
This stuff feels arcaneish
i dont get anything :(
very sleepy bg music
How each clique containing all of the colors makes set of v-colored vertices a vast independent set?
I'm confused at 7:23. Do you mean G complement doesn't have an independent set with a vertex in each maximum clique? Because by lemma 1 the original G must have one.
Edit: I watched with the subtitles and they clearly say G complement and you translate between the two... It is a bit confusing.
At 8:42, I don't see why that has tp be true. If you were to color every vertex from a max independent set with the same color then you would have to color every max independent set a different color, but maybe there could exist a better coloring that doesn't assign the same color to the vertices from the same max independent set.
Let's say that there is some better coloring than the one I described (that uses the independent sets). Since this coloring has less colors, the number of vertices of at least one of its colors will have to be greater than the size of the maximum independent set, which is a contradiction (since it would be a bigger maximum independent set).