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A disproof of Henning's conjecture on irredundance perfect graphs

Lutz Volkmann, Vadim E. Zverovich
2002 Discrete Mathematics  
We also give a summary of known results on irredundance perfect graphs. Moreover, the irredundant set problem and the dominating set problem are shown to be NP-complete on some classes of 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.  ...  A proof or disproof of this conjecture would be a great contribution towards a characterization of irredundance perfect graphs.  ... 
doi:10.1016/s0012-365x(01)00300-4 fatcat:glnxbp3y6zge5nyq27wy4boaty

Page 3210 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
Mynhardt (3-VCTR-MS; Victoria, BC) COMBINATORICS 2003e:05104 05C69 Volkmann, Lutz (D-AACH-M2; Aachen) ; Zverovich, Vadim E. (4-BRNL; Uxbridge) A disproof of Henning’s conjecture on irredundance perfect  ...  A graph G(V, E) is called irredundance perfect if ir( 7) = y(H) for every induced subgraph H of G. M. A.  ... 

Page 180 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
A. see Kabanov, Vladislav Vestergaard, Preben Dahl see Tuza, Zsolt, 2003):05095 Volkmann, Lutz (with Zverovich, Vadim E.) A disproof of Henning’s conjecture on irredundance perfect graphs.  ...  (English summary) 2003e:05104 — A remark on g-dominating cycles. (English summary) 2003¢:05167 — (with Zverovich, Vadim E.) Proof of a conjecture on irredundance perfect graphs.  ... 

Page 2196 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
A disproof of Henning’s conjecture on irredundance perfect graphs. (English summary) Discrete Math. 254 (2002), no. 1-3, 539-554.  ...  Proof of a conjecture on irredundance perfect graphs. (English summary) J. Graph Theory 41 (2002), no. 4, 292-306.  ...