Euler Paths & the 7 Bridges of Konigsberg | Graph Theory

An Euler Path walks through a graph, going from vertex to vertex, hitting each edge exactly once. But only some types of graphs have these Euler Paths, it depends on the degree of the vertices. We state and motivate the big theorem, and then use it to solve the infamous 7 bridges of Konigsberg problem that motivated Euler to start studying graph theory.

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[baotrantruong]

Thank you so much! Yours is the first video I found that actually breakdown the logic of in-out and why there has to be 2 odd vertices.

[thStringanishmandal]

you're going great, the way you give explanation touches the every contents and brings easy to understand

[joneswafula]

Trefor: Pause the video and try it out and see
Me: Pauses videos and struggles to find path for 45 mins
Trefor: It is impossible!!
Love you guy! I feel like I owe you tuition fees or something

[amrel-demerdash]

What about If E= {(A, C), (A, B), (B, C), (C, B)} then the degree of A = 2, B = 3, c = 3 and you have a Euler path (C -> A -> B -> C -> B)?
I googled it and found "if a graph is connected and has exactly 2 odd vertices then it has an Eurlerian path "

[novanuke]

I was really hoping this was a computer science channel because this concept was explained so well. Keep up the good work!

[MTHU]

It's so interesting that there's an impossibility in human creation. I wonder if they ended up building another bridge to solve the problem.

[ArpanDasgupta-qn]

Suppose I remove one edge connecting AB. Consider path CBDBAC. Isn't this an Euler circuit? Why doesn't this contradict the Theorem at 4:45?

[prithujsarkar]

Can you share me the video link where you told this 5:20
i am curious to see the proof of the other direction of this statement

[MagnusTheUltramarine]

At 4:35 you say that if it even has 1 vertex with odd degree, then there is no Euler Circuit, but isn't that contrary to what you said before, that if it starts odd and the last vertex is also odd, but everything in the middle is even, then there is an Euler Circuit.
For example: Take ABCDE, A and E have 3 vertices, but BCD have two (A:B, A:C, A:D, B:E, C:E, D:E), you can have an Euler Circuit

[nathansudermann-merx]

Great explanation, great visualization. Thank you.

[shrutinehra]

solve 👇⬇️
In seven bridges problem, was it possible for citizen of Konigsberg to make a tour of the city and cross each bridge exactly twice? Give reason

[yaarrated]

So you are saying that if we have two vertices (start and end) with odd degree and every other vertices with even degree, then the Euler path is possible? Oh that is interesting

[nadred]

What if you took out two Edges from A to B and B to C, wouldn't some vertices be odd degree and and Euler path be possible? Or does that not count because you went to A twice? But you didn't use the edge twice?

[austino_climbs]

Really good video and well explained! Thanks!

[tanug]

Well explained👏👏
Thank you so much it was worth watching 😍

[felipesalvador]

In the six-bridge problem as shown by the graph below, how many ways are there of traversing all six bridges (shown as edges here) exactly once?

[jargomanihilda]

He pronounces Euler as oiler, I call it a YOU-ler