Given D and H two digraphs, D is H-coloured iff the arcs of D are coloured with the vertices of H. After defining what do we mean by an H-walk in the coloured D, we characterise those H, which we call panchromatic patterns, for which all D and all H-colourings of D admit a kernel by H-walks. This solves a problem of Arpin and Linek from 2007.
Cite
@article{arxiv.1504.06596,
title = {On Panchromatic Patterns},
author = {Hortensia Galeana-Sanchez and Ricardo Strausz},
journal= {arXiv preprint arXiv:1504.06596},
year = {2015}
}