## Abstract A __quasiβkernel__ 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. ChvΓ‘tal and LovΓ‘sz proved that every digraph has a quasiβkernel. Recently, Gutin et al. raised the question o
About quasi-kernels in a digraph
β Scribed by H. Jacob; H. Meyniel
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 122 KB
- Volume
- 154
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
We generalize a result by Maghout who had shown that every tournament of radius 2 admits three distinct centers. Here we prove that every graph without kernel has at least three distinct quasi-kernels.
π SIMILAR VOLUMES
## Abstract A vertex set __X__ of a digraph __D__β=β(__V, A__) is a __kernel__ if __X__ is independent (i.e., all pairs of distinct vertices of __X__ are nonβadjacent) and for every __v__ β __V__β__X__ there exists __x__ β __X__ such that __vx__ β __A__. A vertex set __X__ of a digraph __D__β=β(__V
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
A closed form solution is provided for the length, relatively between two vertices of a quasi strongly connected digraph. to a potential Cr, of a chain ## I. Detidtions and nobtion!!i Let G = (V, A) denote a finite connected digraph without loop; V is the set of vertices and A the set of arcs. A