A digraph D is said to be an R-digraph (kernel-perfect graph) if all of its induced subdigraphs possesses a kernel (independent dominating subset). I show in this work that a digraph D, without directed triangles all of whose odd directed cycles C = (1, 2,..., 2n + 1, 1), possesses two short chords
A counterexample to a conjecture of meyniel on kernel-perfect graphs
✍ Scribed by Hortensia Galeana-Sánchez
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 237 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Comnnmicated by G. Berge In [3] Galeana-Stinchez and Neumann-Lara have deveioped a genera! method to extend kernel-perfect graphs to kernel-perfect critical graphs. In this note we construct a class of kernel-perfect critical graphs which can be used to extend any kernel-perfect graph. For gen
Chilakamarri, K.B. and P. Hamburger, On a class of kernel-perfect and kernel-perfect-critical graphs, Discrete Mathematics 118 (1993) 253-257. In this note we present a construction of a class of graphs in which each of the graphs is either kernel-perfect or kernel-perfect-critical. These graphs or
The bondage number h(G) of a nonempty graph G was first introduced by Fink, Jacobson, Kinch and Roberts in [3]. They generalized a former approach to domination-critical graphs, In their publication they conjectured that b(G)<d(G)+ 1 for any nonempty graph G.
## Abstract Let __ir__(__G__) and γ(__G__) be the irredundance number and the domination number of a graph __G__, respectively. A graph __G__ is called __irredundance perfect__ if __ir__(__H__)=γ(__H__), for every induced subgraph __H__ of __G__. In this article we present a result which immediatel