Something seems to be very strange and suspicious about the author of the paper. The paper has appeared in print:

http://link.springer.com/article/10.1134%2FS0032946014040048

Yet I know that the paper was submitted to a very respectable non-russian journal and was rejected due to a trivial errors and invalid assumptions in the first pages. 

It does look strange that the author keeps posting and posting solutions to very famous problems in combinatorics every few months or so (yesterday a paper appeared claiming to have solved the famous conjecture on the singularity probability of a random Bernoulli matrix) and they all appear in 1 journal or do not appear at all. As the length of papers is 10-15 pages and they claim to solve long standing open problems, I would expect the refereeing process to be lightning fast and the best journals trying to snap those papers as soon as possible. Yet it does not happen, which indicates that the proofs are probably incorrect and no one wants to referee the terrible write-ups again. 

The papers genuinely terribly written (I have looked at them all quite a bit as I am interested) and no effort seems to have been put in making the results more readable. It is therefore strange that the author keeps posting and posting new supposed breakthroughts without making the previous ones more accessible (if the proofs are correct, hordes of combinatorialists and probabilists would be lining up to read it and present it in seminar, but we have absolute silence instead). 

But this is only my opinion. I would be very glad that is gloomy outlook is misplaced.