Discovery about Book Embedding of Graphs - Numberphile

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NUMBERPHILE

Videos by Brady Haran
Animation and Editing by Pete McPartlan

Special error correction credits to Numberphile Society members Michael Colognori & Debbie Chakour

[ericvilas]

it's really fascinating how similar this feels to the 4-color theorem: you have a planar graph that can be categorized into parts that can behave in two different ways depending on the number of parts (either you need x parts or you need fewer than/more than x parts to fully categorize it) and proving the case for x=3 and x=5 was relatively straightforward but it took a lot of extra time to prove x=4

[PureZOOKS]

Dr Grime absolutely my favourite regular on this channel.
He knows how to explain things so well that a kid can understand it, and he knows how to scale explanations from the basics up until the higher level stuff.
Also, his awkward and enthusiastic demeanour reassures me that he is a real mathematician and a nerd.

[Axacqk]

It's not every day that an explicit solution to a graph problem is found that can be printed on less than all the paper in the universe, one vertex per proton.

[taygrew]

I just find it how mind blowing life seems come full circle(-ish). I started watching this channel back in early middle school and Dr Grime was one of the first people on this channel that really stuck with me, and now i'm only a couple semesters away from graduating with my undergrad in Math. I loved growing up with this channel<3 thank you for what and everyone that's ever contributed do!

[TheMrJHolden]

Brady's graphics are the genius of numberphile videos! His interviews are amazing and the knowledge he shares needs to go further. singingbanana needs more sunshine.

[typha]

I did a project in college specifically about looking at books of knots, every knot can be done with 3 pages (and apart from the unknot they all need 3 pages) so they're a little boring with that respect, but the proof of this is rather simple, and then from there you can give each arc it's own page and that's the arc representation of a knot, and then there's a pretty simple proof of Alexander's theorem using that representation. Just fun stuff.

[beefchicken]

I’m Canadian, but my parents are from northern England. One particular room in my childhood home had two cupboards, one that contained boots, winter jackets, and mittens. That was the “boot cupboard”. The other cupboard in this room was where we kept our books. That was the “book cupboard”. It was a source of constant confusion.

[jasonsteverson]

I love this! Reminds me of the early Numberphile videos. I'm far from a mathematician, but in this instance, simplicity with everyday understanding makes for a great video that really appeals to a dummie like me. And, James is the best at this stuff. What a great teacher. Thanks for this video, Brady!

[brianbouchard]

That was the most beautiful graph I’ve ever seen. What a reveal!

[AnHebrewChild]

Great graphics Mr Grime! This channel has only gotten better.

[minamagdy]

Fun fact: a tree can always be done in only one page. Pick a root, and place it on the leftmost point. Afterwards, place all the points of the graph in a depth-first listing, and connect all points. Every subtree will be all together, recursively listed without intersections in the single page.

[Nekonaut_aka_Jebus]

yo i've actually drawn a similar number line by hand before! glad to know i wasn't the only one that had the idea of doing that lol

[Generalth]

Hi Dr. Grime! Hi Brady!

This was really nicely explained. What an interesting problem! It's great to see someone found a solution once and for all.

[shufflecat]

In this video I learned something about graph theory, and unlearned how I said the word book. Balanced, as all things should be.

[Thejosiphas]

haven't watched this channel in many years and i am relieved to see that james grimes is still very handsome

[jj.wahlberg]

I am a simple girl. I see James, I click.

[dashmore]

Freeze the video at 7:46 and check out those eye popping numbers on the screen on the wall! 4000+ videos and 1.3 billion views. Way to go Brady and team!

[bertblankenstein]

Instantly thinking about the infamous problem where the points define electricity, water, and gas, and each of the homes need to be connected to each one, without crossing (on a regular sheet of paper).

[ggrocks]

It's a good day when James is on numberphile 😁

[tombaker]

Canteieve ive been watching this guy for 10 years