Proof: Two Longest Paths Have a Common Vertex | Graph Theory, Connected Graphs

Support the production of this course by joining Wrath of Math to access all my graph theory videos!    / @wrathofmath   🛍 Check out the coolest math clothes in the world: https://mathshion.com/ Graph Theory course:    • Graph Theory   Graph Theory exercises:    • Graph Theory Exercises   Get the textbook! https://amzn.to/3HvI535 In any connected graph, two longest paths will always have a common vertex! We'll prove this theorem in today's video graph theory lesson using contradiction! We suppose we have two longest paths in a connected graph that do NOT have a common vertex, and we'll be able to find a longer path, producing a contradiction! ◆ Support Wrath of Math on Patreon:   / wrathofmathlessons   Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu