The paper by Ron Graham and Bruce Rothschild which gives a really short proof (involving a complicated triple induction) of van der Waerden's theorem:

R.L. Graham and B.L. Rothschild, A short proof of van der Waerden's theorem on arithmetic progressions, Proc. American Math. Soc. 42(2) 1974, 385–386.

http://www.ams.org/journals/proc/1974-042-02/S0002-9939-1974-0329917-8/S0002-9939-1974-0329917-8.pdf

The paper by Ron Graham and Bruce Rothschild which gives a really short proof (involving a complicated triple induction) of van der Waerden's theorem:

R.L. Graham and B.L. Rothschild, A short proof of van der Waerden's theorem on arithmetic progressions, Proc. American Math. Soc. 42(2) 1974, 385–386.

https://www.ams.org/journals/proc/1974-042-02/S0002-9939-1974-0329917-8/S0002-9939-1974-0329917-8.pdf

The paper by Ron Graham and Bruce Rothschild which gives a really short proof (involving a complicated triple induction) of van der Waerden's therem:

R.L. Graham and B.L. Rothschild, A short proof of van der Waerden's theorem on arithmetic progressions, Proc. American Math. Soc. 42(2) 1974, 385–386.

The paper by Ron Graham and Bruce Rothschild which gives a really short proof (involving a complicated triple induction) of van der Waerden's theorem:

R.L. Graham and B.L. Rothschild, A short proof of van der Waerden's theorem on arithmetic progressions, Proc. American Math. Soc. 42(2) 1974, 385–386.

http://www.ams.org/journals/proc/1974-042-02/S0002-9939-1974-0329917-8/S0002-9939-1974-0329917-8.pdf