We define a fractional version of the notion of ``kernels'' in digraphs and prove that every clique acyclic digraph (i.e., one in which no clique contains a cycle) has a fractional kernel. Using this we give a short proof of a recent result of Boros and Gurvich (proving a conjecture of Berge and Duc
Kernels in Weighted Digraphs
✍ Scribed by Ron Aharoni, Eli Berger, Irina Gorelik
- Book ID
- 120755382
- Publisher
- Springer Netherlands
- Year
- 2013
- Tongue
- English
- Weight
- 304 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0167-8094
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📜 SIMILAR VOLUMES
We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A directed path is called monochromatic if all of its arcs are coloured alike. A directed cycle is called quasi-monochromatic if with at most one exception all of its arcs are coloured alike. A set N C\_\_ V(D)
## Abstract A __quasi‐kernel__ in a digraph is an independent set of vertices such that any vertex in the digraph can reach some vertex in the set via a directed path of length at most two. Chvátal and Lovász proved that every digraph has a quasi‐kernel. Recently, Gutin et al. raised the question o