Packing of rigid spanning subgraphs and spanning trees

Packing of rigid spanning subgraphs and spanning trees

We prove that every (6k + 2`, 2k)-connected simple graph contains k rigid and ` connected edge-disjoint spanning subgraphs. This implies a theorem of Jackson and Jordán [4] and a theorem of Jordán [6] on packing of rigid spanning subgraphs. Both these results are generalizations of the classical result of Lovász and Yemini [9] saying that every 6-connected graph is rigid for which our approach ...

Packing of 2-Connected Spanning Subgraphs and Spanning Trees

We prove that every (6k + 2`, 2k)-connected simple graph contains k rigid and ` connected edgedisjoint spanning subgraphs. This implies a theorem of Jackson and Jordán [4] and a theorem of Jordán [6] on packing of rigid spanning subgraphs. Both these results are generalizations of the classical result of Lovász and Yemini [9] saying that every 6-connected graph is rigid for which our approach p...

Spanning trees in subgraphs of lattices

Domination game played on trees and spanning subgraphs

The domination game, played on a graph G, was introduced in [3]. Vertices are chosen, one at a time, by two players Dominator and Staller. Each chosen vertex must enlarge the set of vertices of G dominated to that point in the game. Both players use an optimal strategy–Dominator plays so as to end the game as quickly as possible, Staller plays in such a way that the game lasts as many steps as ...

Reconfiguring spanning and induced subgraphs

Subgraph reconfiguration is a family of problems focusing on the reachability of the solution space in which feasible solutions are subgraphs, represented either as sets of vertices or sets of edges, satisfying a prescribed graph structure property. Although there has been previous work that can be categorized as subgraph reconfiguration, most of the related results appear under the name of the...