A theorem about a conjecture of H. Meyniel on kernel-perfect graphs

About the Strong Perfect Graph Conjecture on circular partitionable graphs

Meyniel Weakly Triangulated Graphs II: A Theorem of Dirac

We generalize a theorem due to Dirac and show that every Meyniel weakly triangu-lated graph has some vertex which is not the middle vertex of any P 5. Our main tool is a separating set notion known as a handle.

On a class of kernel-perfect and kernel-perfect-critical graphs

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 originate from the theory of games (Von Neumann and Morgenstern). We also find criteria to distingui...

A disproof of Henning's conjecture on irredundance perfect graphs

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 paper we disprove the known conjecture of Henning [3, 11] that a graph G is irredundance perfect if and only if ir(H) = γ(H) for every induced subgraph H of G with ir(H) ≤ 4. We also give a summar...

Proof of a conjecture on irredundance perfect graphs

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 immediately implies three known conjectures on irredundance perfect graphs.