Existence of a P2k+1-decomposition in the Kneser graph KGt,2

In this paper, it is shown that if t≡0,1,2 or 3(mod 8k), k≥2, then the Kneser graph KGt,2 can be decomposed into paths of length 2k. Consequently, we obtain the following: for k=2ℓ, ℓ≥1, the Kneser graph KGt,2 has a P2k+1-decomposition if and only if t≡0,1,2 or 3  (mod 2ℓ+3). Using this, the main result of the paper (Whitt III and Rodger, 2015) is deduced as a corollary.