In this work, we investigate the total and edge colorings of the Kneser graphs K(n, s). We prove that the sparse case of Kneser graphs, the odd graphs \(O_k=K(2k-1,k-1)\), have total chromatic number equal to \(\Delta (O_k) + 1\). We prove that Kneser graphs K(n, 2) verify the Total Coloring Conjecture when n is even, or when n is odd not divisible by 3. For the remaining cases when n is odd and divisible by 3, we obtain a total coloring of K(n, 2) with \(\Delta (K(n,2)) + 3\) colors when \(n \equiv 3~\hbox {mod}~4\), and with \(\Delta (K(n,2)) + 4\) colors when \(n \equiv 1~\hbox {mod}~4\). Furthermore, we present an infinite family of Kneser graphs K(n, 2) that have chromatic index equal to \(\Delta (K(n,2))\).

在这项工作中，我们研究了 Kneser 图K ( n ,  s )的总着色和边着色。我们证明了 Kneser 图的稀疏情况，奇数图\(O_k=K(2k-1,k-1)\) 的总色数等于\(\Delta (O_k) + 1\)。我们证明了当n为偶数或当n为奇数不能被 3 整除时，Kneser 图K ( n , 2) 验证了总着色猜想。 对于n为奇数且可被 3 整除的其余情况，我们获得了一个总着色猜想K ( n , 2) 与\(\Delta (K(n,2)) + 3\)颜色，当\(n \equiv 3~\hbox {mod}~4\)和\(\Delta (K(n,2)) + 4\)颜色当\(n \equiv 1~\hbox {mod}~ 4\)。此外，我们提出了一个无穷大族 Kneser 图K ( n , 2) ，其色度指数等于\(\Delta (K(n,2))\)。