KP-digraphs and CKI-digraphs satisfying the k-Meyniel's condition

A digraph D is said to satisfy the k-Meyniel’s condition if each odd directed cycle of D has at least k diagonals. The study of the k-Meyniel’s condition has been a source of many interesting problems, questions and results in the development of Kernel Theory. In this paper we present a method to construct a large variety of kernel-perfect (resp. critical kernel-imperfect) digraphs which satisfy the k-Meyniel’s condition. Primary keywords: digraph, kernel, independent set of vertices, absorbing set of vertices, kernel-perfect digraph, critical-kernel-imperfect digraph, τ -system, τ 1 -system. Secondary keywords: indepedent kernel modulo Q, co-rooted tree, τ -construction, τ 1 -construction. 1991 Mathematics Subject Classification: 05C20.