Intro to Tournament Graphs | Graph Theory

We introduce directed tournament graphs, which can be thought of as a graph representing the outcome of a round robin tournament - where vertices represent teams, and directed edges (arcs) go from winners to losers. We'll also discuss how many labelled tournaments there are on n vertices, and how many unlabelled tournaments there are. #GraphTheory
We see several explanations and examples of tournament graphs, and some non-examples. A tournament is a directed graph with exactly one arc between each pair of vertices. Or equivalently, it is an orientation of a complete graph.
Orientations of Graphs: • Orientations of Graphs...
Number of edges in a complete graph: • Number of Edges in a C...
Transitive Tournaments: • Transitive Tournaments...
Tournament is Transitive iff No Cycles: • Proof: Tournament is T...
Every Tournament has Hamiltonian Path: • Proof: Every Tournamen...
Graph Theory playlist: • Graph Theory
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[@WrathofMath]

CORRECTION: Around 8:40 I show the only two tournaments with n=3. The tournaments shown are isomorphic by mistake. The two tournaments with n=3 are the cycle graph C3 (not depicted by mistake) and the graph I accidentally drew twice.

[@PunmasterSTP]

I've come across some graph theory over the years, but I don't ever recall learning the term "tournament graph". Cool stuff!

[@peterburbery2341]

Can you make some videos on graph types?
This is really helpful explanation.
For example, maybe a video covering sunlet graphs, gear graphs, etc.

[@EHTFS]

Great video! This helped me a ton with my discrete mathematics class. Can't believe it doesn't have more views!

[@WrathofMath]

Thank you, so glad it helped! I thought it'd have more views too - I had a lot of fun making my videos on tournaments, if you check out my graph theory playlist you'll see several more on this topic. I'm sure over time it will gain traction. It is a niche topic though!
czcams.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html

[@aashsyed1277]

nice video!- thank you so so much!!!!!!!!!

[@WrathofMath]

Of course, great to finally start talking about tournament graphs - it's long overdue!

[@aznnguyen20]

Can you make a lesson on blocks?

[@JurgenN-cu9st]

There is a mistake in the example for the non-isomorphic tournaments: in the case n=3, the depicted graphs are actually isomorphic.

[@WrathofMath]

Thanks, pinned comment about it!

[@mohammadrezajavadi3498]

Well done

[@WrathofMath]

Thank you!

[@ridwanulhasantanvir6456]

7:05 2^(nc2)

[@oiciruamlau4795]

Lol you scared me when you said the last eg the k4 was not a tournament

[@WrathofMath]

Haha, classic gag! Thanks for watching!