Connected Domination and Spanning Trees with Many Leaves
SIAM Journal on Discrete Mathematics
Extremal Graph Theory
Upper bounds on the k-domination number and the k-Roman domination number
Discrete Applied Mathematics
Bounds on the connected k-domination number in graphs
Discrete Applied Mathematics
On the Hull Number of Triangle-Free Graphs
SIAM Journal on Discrete Mathematics
Note: On upper bounds for multiple domination numbers of graphs
Discrete Applied Mathematics
| Hi-index | 0.00 |
Let F = {G1, …, Gt} be a family of n-vertex graphs defined on the same vertex-set V, and let k be a positive integer. A subset of vertices D ⊂ V is called an (F, k)-core if, for each v ∈ V and for each i = 1, …, t, there are at least k neighbours of v in Gi that belong to D. The subset D is called a connected (F, k)-core if the subgraph induced by D in each Gi is connected. Let δi be the minimum degree of Gi and let δ(F) = minti=1δi. Clearly, an (F, k)-core exists if and only if δ(F) ≥ k, and a connected (F, k)-core exists if and only if δ(F) ≥ k and each Gi is connected. Let c(k, F) and cc(k, F) be the minimum size of an (F, k)-core and a connected (F, k)-core, respectively. The following asymptotic results are proved for every t k F. The results unify and extend related results on dominating sets, strong dominating sets and connected dominating sets.