Thank you for this! Recently been playing some brain games on my phone and this is one of the games, up to level 200 in 2 days only 40 levels left /: I’ve been solving these without even knowing the whole backstory and paths kind of just clicked in my head
@@aayushperecharla3486 the app is called impulse, and the game I liked and finished at the time is called draw one line, there are 235 levels for it that I finished, but there are multiple free games to play on there that are great. You don’t have to pay to play any of it unless you want to with no ads I hope this helps!
In 3:13 , path in graph theory is define as a graph where no edge and vertice are repeated. So, how come the given diagram is a Euler path? as you've repeated the vertice having three edges more than one time.
@Deepak Hariharan Neither is it allowed in a Hamiltonian path. There, you are allowed to only visit each vertex once as you can see in the third example
take a look at its degree, it has an euler path because there are such 2 odd degrees each vertices. we have this concept that it is not actually an euler path if it exceed it into 2 above. but in this case, there are 2 odd degrees each vertices and one has 4. so we can now conclude it as euler path but no circuit.
The reason that one is not Hamiltonian is because to get to every vertex would require using a vertex more than once. To have a Hamiltonian path, each vertex is is used exactly once.
Aren't you talking about the more general case of an Euler trail here? A trail is defined as a walk in which no edge is traversed more than once, but in which a vertex can appear more than once. A path is where each edge and each vertex appears at most one time. Your second example using the multigraph is an Euler trail, not an Euler path.
But in tracing out the 6 edges you hit the bottom two vertices (call them a and b) twice and the top vertex (c) 3 times, so its a trail, not a path: a (ac)_1 c (ca)_2 a (ab) b (bc)_1 c (cb)_2 b (bc)_3 c.
how can a hamilton circuit vistit a vertex once and also start and end at the same vertex. If it starts and ends at the same vertex, the vertex was visited twice.
Such a clear explanation! And great examples! Thank you, sir!
Thank you for your kind words. My pleasure.
Hi
yeah, it really helps for my notes and my finals next week
Quick and concise explanation. Appreciate it!
I'm glad it was useful.
Thank you Sir, very useful tutorial. Especially the Konigsberg problem.
This is why I love to learn from Western professors
thank you so much for such a clear explanation
YOU'RE A REAL LIFE SAVER SIR!!!
I'm glad you found it useful. Thank you for your encouragement.
This is the video i looking for.
Well explained! 2h lecture in 10 min ;)
Ola Kaszuba thank you.
Thank you for this! Recently been playing some brain games on my phone and this is one of the games, up to level 200 in 2 days only 40 levels left /: I’ve been solving these without even knowing the whole backstory and paths kind of just clicked in my head
what game is this? Sounds interesting.
@@aayushperecharla3486 the app is called impulse, and the game I liked and finished at the time is called draw one line, there are 235 levels for it that I finished, but there are multiple free games to play on there that are great. You don’t have to pay to play any of it unless you want to with no ads I hope this helps!
In 3:13 , path in graph theory is define as a graph where no edge and vertice are repeated.
So, how come the given diagram is a Euler path? as you've repeated the vertice having three edges more than one time.
Have a great day sir.
It was a nice video
Really sir you are best lecturer
Thank you! You explained it very well.
Thanks a lot! Wonderful explanation.
Thanks so much! I finally understand it
Great explanation, thank you so much
My pleasure.
simple and smart teaching
Thank you so much! Explenation was great!!
Well Explained & Thanks a lot !
Interestingly, adding any one additional bridge makes the Königsberg problem soluble.
I loved it!!
how to figure out odd degree? Please response
at 6:42 if we start with vertex a, will we get a hamiltonian path that covers all vertices????? pleassseee replyyy
@Deepak Hariharan if we start at 'a' to reach 'e', 'a' should be revisited right???? then how will there be a path???
@Deepak Hariharan Neither is it allowed in a Hamiltonian path. There, you are allowed to only visit each vertex once as you can see in the third example
I love the explanation! But...are you related to the Olsen twins? ;D
Can you help us to solve my problem Euler paths and circuit?
3:52 should be “has Euler trail but no Euler path cuz you go through every edge only one time each
take a look at its degree, it has an euler path because there are such 2 odd degrees each vertices. we have this concept that it is not actually an euler path if it exceed it into 2 above. but in this case, there are 2 odd degrees each vertices and one has 4. so we can now conclude it as euler path but no circuit.
very helpful tutorial
excellent lecture, thank u
Thanks for the vid
You are welcome.
Thank you so much!
at 7:07 the graph is a Hamiltonian. Because it uses every vertex ones. why you said no? I am confused
The reason that one is not Hamiltonian is because to get to every vertex would require using a vertex more than once. To have a Hamiltonian path, each vertex is is used exactly once.
Thank you
Amazing
Aren't you talking about the more general case of an Euler trail here? A trail is defined as a walk in which no edge is traversed more than once, but in which a vertex can appear more than once. A path is where each edge and each vertex appears at most one time. Your second example using the multigraph is an Euler trail, not an Euler path.
Jerome Malenfant yes there are 'trails.' I do believe my second example is an example of an Euler path.
But in tracing out the 6 edges you hit the bottom two vertices (call them a and b) twice and the top vertex (c) 3 times, so its a trail, not a path:
a (ac)_1 c (ca)_2 a (ab) b (bc)_1 c (cb)_2 b (bc)_3 c.
tnx!
how can a hamilton circuit vistit a vertex once and also start and end at the same vertex. If it starts and ends at the same vertex, the vertex was visited twice.
Thank you 😊
Thanks sir
Thanks!
Thanks
thumbs up👍
👍
I love you
wish you were my math lecturer
You are too kind. You could come to Western Illinois University and take a class with me. 😉
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Lun py char
sir your sound is so slow and not clear
Such a clear explanation! And great examples! Thank you, sir!
Amazing