Unsolved Problems in Graph Theory

[@lyrimetacurl0]

"look at this graph"

[@natepolidoro4565]

Great quality video. I love this channel.

[@marcelob.5300]

Absolutely, they deserve 1M subscribers

[@Busybody007]

amazing animation soo easy to understand.

[@Fepo.productions]

Me, who is supposed to revise GCSE level maths for my mocks Random video explaining a maths concept I didn't even think could be thought up in fiction Me: hmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

[@ThoughtThrill365]

They are unsolved for a reason 😄

[@davethesid8960]

0:18 - That's why in Hungarian we say "gráf" and "grafikon" to distinguish them.

[@patrickgambill9326]

These are great! Do you like the switching reconstruction and vertex reconstruction problems?

[@marcelob.5300]

Great content!

[@patrickgambill9326]

9:58 What about the graph with no edges? Aren't the chromatic and total chromatic number the same?

[@nivpearlman6514]

Delta(G)=0 X(G)=X''(G)=1 They are the same but trivially and equal to one

[@patrickgambill9326]

Makes sense. I definitely misheard the video. They said maximum degree, not ordinary chromatic number 😅

[@isavenewspapers8890]

This is an interesting edge case (no pun intended). For any edgeless graph, the chromatic number and the total chromatic number are either both 0 or both 1 (and hence the same number). The former arises only in the case of the unique graph with no vertices-the order-zero graph. After all, the graph vacuously starts out with every vertex and edge colored, so we don't need to pick up a single crayon. What about the maximum degree of this graph? Finding a graph's maximum degree amounts to finding the maximum of the set of the degrees of its vertices. But if you take the set of the degrees of the vertices of the order-zero graph, you just get the empty set. You can't take the maximum of the empty set, so the maximum degree of the order-zero graph is undefined. ... At least, I think that's how it works. For a more airtight answer, I'd probably need to be more careful about some of the formal definitions.

[@Dravignor]

Where's the graph isomorphism problem?

[@omfgacceptmyname]

divine ambitions? really weird way to say that 5:15 this whole section was strange

[@oserodal2702]

A category is just a funny graph with a few rules. Why not do unsolved problems for category theory?