Graph Theory 3: Hamiltonian Paths & Ore's Theorem

[@匿名者-q6j]

Again! What a wonderful lesson. It's always this kind of lessons make me fall in love with math even when there's a math exam.

[@shaaravguha3760]

Isn't that W example near the end hamiltonian? If you take the bottom 2 vertices as your u and v then it 6 which is greater then 5, I've found quite a few hamiltonian circuits as well.

[@stuspivack]

If Ore's theorem is "D(U)+D(V)>=n ==> Hamiltonian circuit exists" then the converse is "Hamiltonian circuit exists ==> D(U)+D(V)>=n"? To disprove that shouldn't we provide an example of a graph with a Hamiltonian circuit for which D(U)+D(V)>/=n ? Your example is a graph with no Hamiltonian circuit, which is not what we need, right?

[@kingshukdutta2064]

The Professor made a graph(pentagon-shaped) where D(U)+D(V)

[@stuspivack]

@@kingshukdutta2064 Oops. It only took him a few seconds to discuss that graph and I must have missed it. When I wrote my comment, I thought he was using the *next* graph he drew to consider the converse of Ore's theorem. Thanks.

[@pizzanachos2323]

Black on black outfit is fire

[@el_andrius]

Beutiful

[@alexaviraghidvegi9319]

Dear God. Please let me pass my oral exam about discrete mathematics tomorrow. Let my prayers be heard. Thank you, God. - A student