https://hal.inria.fr/hal-01184456Galeana-Sánchez, HortensiaHortensiaGaleana-SánchezUNAM - Instituto de Matematicas - UNAM - Universidad Nacional Autónoma de México = National Autonomous University of MexicoGuevara, Mucuy-KakMucuy-KakGuevaraUNAM - Instituto de Matematicas - UNAM - Universidad Nacional Autónoma de México = National Autonomous University of MexicoKernel perfect and critical kernel imperfect digraphs structureHAL CCSD2005kernelsemikernelsemikernel modulo Fkernel perfect digraphcritical kernel imperfect digraph[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM][MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO][INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC]Episciences Iam, CoordinationStefan Felsner2015-08-17 10:48:102022-08-08 17:38:052015-08-17 15:39:16enConference papershttps://hal.inria.fr/hal-01184456/document10.46298/dmtcs.3467application/pdf1A kernel $N$ of a digraph $D$ is an independent set of vertices of $D$ such that for every $w \in V(D)-N$ there exists an arc from $w$ to $N$. If every induced subdigraph of $D$ has a kernel, $D$ is said to be a kernel perfect digraph. Minimal non-kernel perfect digraph are called critical kernel imperfect digraph. If $F$ is a set of arcs of $D$, a semikernel modulo $F$, $S$ of $D$ is an independent set of vertices of $D$ such that for every $z \in V(D)- S$ for which there exists an $Sz-$arc of $D-F$, there also exists an $zS-$arc in $D$. In this talk some structural results concerning critical kernel imperfect and sufficient conditions for a digraph to be a critical kernel imperfect digraph are presented.