About (k,l)-kernels, semikernels and Grundy functions in partial line digraphs
Camino Balbuena, Hortensia Galeana‐Sánchez, Mucuy Guevara · Discussiones Mathematicae Graph Theory · 2018
Let D be a digraph of minimum in-degree at least 1.We prove that for any two natural numbers k, l such that 1 ≤ l ≤ k, the number of (k, l)-kernels of D is less than or equal to the number of (k, l)-kernels of any partial line digraph LD.Moreover, if l < k and the girth of D is at least l+1, then these two numbers are equal.We also prove that the number of semikernels of D is equal to the number of semikernels of LD.Furthermore, we introduce the concept of (k, l)-Grundy function as a generalization of the concept of 1