Proof: Regular Bipartite Graph has a Perfect Matching | Graph Theory

Support the production of this course by joining Wrath of Math to access all my graph theory videos! https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 🛍 Check out the coolest math clothes in the world: https://mathshion.com/ Graph Theory course: https://www.youtube.com/playlist?list=PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH Graph Theory exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxXtYASoshtU3yEKqEmo1o1L Get the textbook! https://amzn.to/3HvI535 An r-regular bipartite graph, with r at least 1, will always have a perfect matching. We prove this result about bipartite matchings in today's graph theory video lesson using Hall's marriage theorem for bipartite matchings. Recall that a perfect matching is a matching that covers every vertex of a graph. Proof that a Regular Bipartite Graph is Balanced: https://www.youtube.com/watch?v=73u0OQCR2rs Matchings, Perfect Matchings, Maximum Matchings, and More: https://www.youtube.com/watch?v=chdr2aj4FUc Hall's Theorem and Condition for Bipartite Matchings: https://www.youtube.com/watch?v=Ihr6gMx7b9c Proof of Hall's Marriage Theorem: https://www.youtube.com/watch?v=4tu-H4ES0fk ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: https://www.patreon.com/join/wrathofmathlessons ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu