day 11

5:49 am, 5 October 3 years. 8:47 am I am going to win SMMC man, not even a question. I just have to.
thinking about ramsey stuff, i proved R(3,4)=9
Ok so i independelty proved R(k,l)<=R(k,l-1)+r(k-1,l)-1 when both are even.
Then i found a really cool construction for 3,4 avoiding coloring of K_8 using this really cool "algorithm" i found.
Basically, you look at a fixed vertex v, say it has 3 red and 4 blue neighbours (you could have 2r, 5b too; but youll see why 3r,4b is better) then you'll have a blue K3 and a triangle free coloring of K4 right.
Now note that v can never be in a red K3 or blue K4 cos obv.
So the rest of the stuff is basically a 7 vertex 3,4 free graph; and then we're splitting it into a blue K3 and a triangle free graph. and the intution is that finding a 7 vertex 3,4 gree graph is much easier.
I mean indeed , just take the 5 vertex R(3,3) graph, and then we have two more vertices a and b. color ab red, and color all other edges of a blue. color all other edges of b blue, except for 2-b which is red. then you can check this is R(4,3). So we have our "split" as 1-3-a as the blue triangle and the rest of it as the triangle free thingy.... This is actually very promising, i mean especially for R(3,n) right... I wanna solve cool math problems, like research math problems. Finding R(3,10) is still open, this would genuinely be cool as fuck. let's keep working rn tho brodie. go win smmc right here. and this is just gonna be the start
btw i think this is genuinely a cool new construction; like the standard construction is the octahedron w/ adjacent and opposite vertiecs red. let's keep thinking. skyscraper geographer playing on loop. im really going to win this time. no regrets mane.

ok i looked at brandon mckay's site, this is so cool. he also invented like graph encoding, like for instance G@hZCc represents a 8 vertex graph. that's genuinely crazy ahaha. bro i still dont know why base16 stuff, like say A for instance takes more size than 0,1 binary, i guess thats got to do with some CS stuff wtv/ Well yeah the graph I had found was G_gqK haha. ok, it would be so cool if i found R(m,n) for some m, n lol. math is actually so fucking crazy man. Well, the graph i found i just drew it out and it's the octagedron with two adjaecnt diagonals.