𝔖 Bobbio Scriptorium
✦   LIBER   ✦

About quasi-kernels in a digraph

✍ 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.

✦ 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.


πŸ“œ SIMILAR VOLUMES


Disjoint quasi-kernels in digraphs
✍ Scott Heard; Jing Huang πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 126 KB

## 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. ChvΓ‘tal and LovΓ‘sz proved that every digraph has a quasi‐kernel. Recently, Gutin et al. raised the question o

On the number of quasi-kernels in digrap
✍ Gregory Gutin; Khee Meng Koh; Eng Guan Tay; Anders Yeo πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 89 KB

## Abstract A vertex set __X__ of a digraph __D__ = (__V, A__) is a __kernel__ if __X__ is independent (i.e., all pairs of distinct vertices of __X__ are non‐adjacent) and for every __v__ ∈ __V__‐__X__ there exists __x__ ∈ __X__ such that __vx__ ∈ __A__. A vertex set __X__ of a digraph __D__ = (__V

Fractional Kernels in Digraphs
✍ Ron Aharoni; Ron Holzman πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 171 KB

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

About the shortest chain between two ver
✍ Jean-Pierre Barthelemy πŸ“‚ Article πŸ“… 1981 πŸ› Elsevier Science 🌐 English βš– 370 KB

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

Almost all digraphs have a kernel
✍ Ioan Tomescu πŸ“‚ Article πŸ“… 1990 πŸ› Elsevier Science 🌐 English βš– 561 KB