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On panchromatic patterns.
- Source :
-
Discrete Mathematics . Oct2016, Vol. 339 Issue 10, p2536-2542. 7p. - Publication Year :
- 2016
-
Abstract
- Since the classic book of Berge (1985) it is well known that every digraph contains a kernel by paths. This was generalised by Sands et al. (1982) who proved that every edge two-coloured digraph has a kernel by monochromatic paths. More generally, given D and H two digraphs, D is H -coloured iff the arcs of D are coloured with the vertices of H . Furthermore, an H -walk in D is a sequence of arcs forming a walk in D whose colours are a walk in H . With this notion of H -walks, we can define H -independence, which is the absence of such a walk pairwise, and H -absorbance, which is the existence of such a walk towards the absorbent set. Thus, an H -kernel is a subset of vertices which is both H -independent and H -absorbent. The aim of this paper is to characterise those H , which we call panchromatic patterns , for which all D and all H -colourings of D admits an H -kernel. This solves a problem of Arpin and Linek from 2007 (Arpin and Linek, 2007). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 339
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 115977578
- Full Text :
- https://doi.org/10.1016/j.disc.2016.03.014