The dichromatic number of an oriented graph is the minimum size of a partition of its vertices into acyclic induced subdigraphs. We prove that oriented graphs with no induced directed path on six vertices and no triangle have bounded dichromatic number. This is one (small) step towards the general conjecture asserting that for every oriented tree T and every integer k, any oriented graph that does not contain an induced copy of T nor a clique of size k has dichromatic number at most some function of k and T.

翻译：方向图形的色数是其脊椎分割成环状诱导子体的最小大小。 我们证明,在6个顶端没有导导导路径且没有三角形的定向图形中,有异色数字是相交的。 这是向一般猜想的一( 小)步, 表明对每个方向树 T 和每个整数 k 来说, 任何不包含导导影的T 或大小 k 的圆块的定向图形, 最多有 k 和 T 的二色数 。