Panchromatic patterns by paths
Germán Benítez-Bobadilla, Hortensia Galeana‐Sánchez, César Hernández‐Cruz · Discussiones Mathematicae Graph Theory · 2022
Let H = (V H , A H ) be a digraph, possibly with loops, and let D = (V D , A D ) be a loopless multidigraph with a colouring of its arcs c :reaches some vertex in S by H-paths, and it is independent by H-paths if no vertex in S can reach another (different) vertex in S by H-paths.A kernel by H-paths is a subset of V D which is independent by H-paths and absorbent by H-paths.We define B 1 as the set of digraphs H such that any H-arc-coloured tournament has an absorbent by H-paths vertex; the set B 2 consists of the digraphs H such that any H-arc-coloured digraph D has an independent,