The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
A set X of vertices of a graph G is said to be 1-dependent if the subgraph of G induced by X has maximum degree one. The 1-dependent Ramsey number t₁(l,m) is the smallest integer n such that for any 2-edge colouring (R,B) of Kₙ, the spanning subgraph B of Kₙ has a 1-dependent set of size l or the subgraph R has a 1-dependent set of size m. The 2-edge colouring (R,B) is a t₁(l,m) Ramsey colouring of Kₙ if B (R, respectively) does not contain a 1-dependent set of size l (m, respectively); in this...
We prove that the smallest cardinality of a maximal packing in any tree is at most the cardinality of an R-annihilated set. As a corollary to this result we point out that a set of parameters of trees involving packing, perfect neighbourhood, R-annihilated, irredundant and dominating sets is totally ordered. The class of trees for which all these parameters are equal is described and we give an example of a tree in which most of them are distinct.
Download Results (CSV)