Every Tree Graph is Bipartite | Graph Theory

Every tree graph is bipartite! Recall that a tree graph is a connected graph with no cycles, thus trees certainly have no odd cycles. Then, since a graph with no odd cycles is bipartite, we have that trees are bipartite. Intro to Tree Graphs: https://www.youtube.com/watch?v=tVuEZakQxhQ Proof that a graph is a tree if and only if every pair of vertices is connected by a unique path: https://www.youtube.com/watch?v=mULsT4CMwYc Proof that a bipartite graph has no odd cycles: https://www.youtube.com/watch?v=xQcCXSFVSks Proof that a graph with no odd cycles is bipartite: https://www.youtube.com/watch?v=_TIqhvDR8DQ Check out the full Graph Theory playlist: https://www.youtube.com/playlist?list=PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH ★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 Thanks to Robert Rennie and Barbara Sharrock for their generous support on Patreon! Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/ Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu My Music Channel: https://www.youtube.com/channel/UCOvWZ_dg_ztMt3C7Qx3NKOQ