Proof: An Edge is a Bridge iff it Lies on No Cycles | Graph Theory
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- เผยแพร่เมื่อ 18 ม.ค. 2020
- An edge of a graph is a bridge if and only if it lies on no cycles. We prove this characterization of graph bridges in today's graph theory lesson!
My lesson on bridges: • What are Bridges of Gr...
Proof that a walk implies a path: • Proof: If There is a u...
Lesson on edge deletion: • Edge Subtraction and B...
We prove the result using contrapositives. Remember the contrapositive of a statement "If P then Q" is "If not Q then not P". The contrapositive of a statement is equivalent to the original statement.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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The outro music is by a friend of mine named Molly Ponkevitch, who, upon my request, kindly gave me permission to use her music in my outros. I usually put my own music in the outros, but I love Molly's music, and wanted to share it with those of you watching. Please check out her wonderful music and other work, as she also does poetry and more.
Molly's TH-cam: / @mollyponkevitch1512
Molly's Website: www.mollyponkevitch.com/
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im doing a degree in computer science and your videos are so helpfull!!!! and thanks for the black background its much easier on the eyes
Thanks a lot sir ... it helps so much .
Thank you for simplifying mathematics concept. Can you make a video for finding the jump models and slide models for different paths. That is \Gamma of P_n.
Awesome , thanks for the help
You're welcome; thanks for watching!
This was a bit wordy but understood in second watch of video after some time.
Very didatic, thanks!
Glad to help!
Hi, LOVE your videos, but I have a question, I am about to take a graph theory exam and I was wondering, for a proof like the one you did in the video, do I need to include both directions of the proof on my test?
Thanks Jazirah! And you need to include whatever is asked of you. If you are asked to prove “If an edge is a bridge, then it lies on no cycles”, then you don’t need both directions because you haven’t been asked for both. But if you’re asked to prove “An edge is a bridge if and only if it lies on no cycles” then you do need both directions, because that is what has been asked for.
How'd your test go?
Sir is there a graph in which an euler line is also a Hamilton circuit
Cycle graph, Euler circuit.
what is an arbitrary vertex..?
An arbitrary vertex of a graph is just any vertex. If we say "let v be an arbitrary vertex of G", then v is just any vertex of G, and otherwise unspecified. As opposed to taking a cut vertex, or a vertex of degree at least 3, for example.
Lies on no cycles? More like "Love listening to these great lectures!" 👍