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A disproof of Henning's conjecture on irredundance perfect graphs

Volkmann, Lutz; Zverovich, Vadim


Lutz Volkmann


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 (Chartrand and Lesniak, Graphs & Digraphs, 3rd Edition, Chapman & Hall, London, 1996, p. 321; Henning, Discrete Math. 142 (1995) 107) 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 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. A number of problems and conjectures are proposed. © 2002 Elsevier Science B.V. All rights reserved.


Volkmann, L., & Zverovich, V. (2002). A disproof of Henning's conjecture on irredundance perfect graphs. Discrete Mathematics, 254(1-3), 539-554.

Journal Article Type Article
Publication Date Jun 10, 2002
Journal Discrete Mathematics
Print ISSN 0012-365X
Publisher Elsevier
Peer Reviewed Not Peer Reviewed
Volume 254
Issue 1-3
Pages 539-554
Keywords mathematics, maths, graphs, Henning, irredundance
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