Euler and Hamiltonian Paths and Circuits

[@annasergienko409]

Such a clear explanation! And great examples! Thank you, sir!

[@DoctorO314]

Thank you for your kind words. My pleasure.

[@youmaylikeit3465]

Hi

[@babyph65]

yeah, it really helps for my notes and my finals next week

[@rasteapure6887]

Thank you Sir, very useful tutorial. Especially the Konigsberg problem.

[@madhurjyadeka5569]

This is why I love to learn from Western professors

[@MehSteven]

Quick and concise explanation. Appreciate it!

[@DoctorO314]

I'm glad it was useful.

[@bibekacharya9586]

thank you so much for such a clear explanation

[@shiva1468]

Really sir you are best lecturer

[@ChandraSekhar-tr7sf]

simple and smart teaching

[@UnrelentingJuggernaut1]

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]

what game is this? Sounds interesting.

[@UnrelentingJuggernaut1]

@@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!

[@olakaszuba]

Well explained! 2h lecture in 10 min ;)

[@DoctorO314]

Ola Kaszuba thank you.

[@ronyspace313]

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.

[@aleksandrkerensky4079]

Interestingly, adding any one additional bridge makes the Königsberg problem soluble.

[@paci.rossy25]

This is the video i looking for.

[@reigngabriellepolvorido6806]

YOU'RE A REAL LIFE SAVER SIR!!!

[@DoctorO314]

I'm glad you found it useful. Thank you for your encouragement.

[@saransappa603]

Thanks a lot! Wonderful explanation.

[@asdasd-ek7nn]

Thank you! You explained it very well.

[@vishnuva2950]

Have a great day sir. It was a nice video

[@JessicaO_BiNdi]

Thanks so much! I finally understand it

[@TeanJodibo]

Great explanation, thank you so much

[@DoctorO314]

My pleasure.

[@kristelgarcia2944]

Can you help us to solve my problem Euler paths and circuit?

[@Damonlia]

Thank you so much! Explenation was great!!

[@richardhernandez8702]

I love the explanation! But...are you related to the Olsen twins? ;D

[@daraxxi757]

how to figure out odd degree? Please response

[@AsiveChowdhury]

Well Explained & Thanks a lot !

[@rajnishsharma2732]

increase the playback speed to and it becomes perfect

[@apporvaarya]

very helpful tutorial

[@vasanth.s1658]

at 6:42 if we start with vertex a, will we get a hamiltonian path that covers all vertices????? pleassseee replyyy

[@vasanth.s1658]

@Deepak Hariharan if we start at 'a' to reach 'e', 'a' should be revisited right???? then how will there be a path???

[@niolee6803]

@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

[@yvsjayanth31]

I loved it!!

[@syedshamail8864]

excellent lecture, thank u

[@femaledeer]

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.

[@jeromemalenfant6622]

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.

[@DoctorO314]

Jerome Malenfant yes there are 'trails.' I do believe my second example is an example of an Euler path.

[@jeromemalenfant6622]

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.

[@mrsrandom3062]

at 7:07 the graph is a Hamiltonian. Because it uses every vertex ones. why you said no? I am confused

[@DoctorO314]

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.

[@sawhenry]

3:52 should be “has Euler trail but no Euler path cuz you go through every edge only one time each

[@ma.patriciaannyabut6539]

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.

[@lekker2333]

Thanks for the vid

[@DoctorO314]

You are welcome.

[@aris.konstantinidis]

Thank you so much!

[@remx11]

Thank you

[@anabildebnath2590]

Amazing

[@mariri.rianaa]

tnx!

[@namelastname7642]

Thank you 😊

[@shekinah4431]

Thanks sir

[@tanveerhasan2382]

Thanks!

[@stephenmufutau-adams7983]

wish you were my math lecturer

[@DoctorO314]

You are too kind. You could come to Western Illinois University and take a class with me. 😉

[@patrycja_1312]

Thanks

[@hibahasan9627]

thumbs up👍

[@sniyamonaharan4735]

👍

[@HeadRecieverAtHeadOffice]

I love you

[@vitocorleone6040]

‘#doge

[@shaheershahzad3871]

Lun py char

[@KapilKumar-qr8hv]

sir your sound is so slow and not clear

[@ahsanakhtar4192]

Such a clear explanation! And great examples! Thank you, sir!

[@anabildebnath2590]

Amazing