par Camby, Eglantine 
;Schaudt, Oliver
Référence Discrete applied mathematics, 177, page (53-59)
Publication Publié, 2014-11
;Schaudt, OliverRéférence Discrete applied mathematics, 177, page (53-59)
Publication Publié, 2014-11
Article révisé par les pairs
| Résumé : | In the first part of this paper, we investigate the interdependence of the connected domination number γc(G) and the domination number γ(G) in some hereditary graph classes. We prove the following results:A connected graph G is (P6,C6)-free if and only if γ c(H)≤γ(H)+1 for every connected induced subgraph H of G. Moreover, there are (P6,C6)-free graphs with arbitrarily large domination number attaining this bound.For every connected (P 8,C8)-free graph G, it holds that γ c(G)/γ(G)≤2, and this bound is attained by connected (P 7,C7)-free graphs with arbitrarily large domination number. In particular, the bound γ c(G)≤2γ(G) is best possible even in the class of connected (P7,C7)-free graphs.The general upper bound of γ c(G)/γ(G)<3 is asymptotically sharp on connected (P9,C9)-free graphs. In the second part, we prove that the following decision problem is Θ2p-complete, for every fixed rational 1 |
