Displaying similar documents to “Conditional resolvability in graphs: a survey.”

Structural Properties of Recursively Partitionable Graphs with Connectivity 2

Olivier Baudon, Julien Bensmail, Florent Foucaud, Monika Pilśniak (2017)

Discussiones Mathematicae Graph Theory


A connected graph G is said to be arbitrarily partitionable (AP for short) if for every partition (n1, . . . , np) of |V (G)| there exists a partition (V1, . . . , Vp) of V (G) such that each Vi induces a connected subgraph of G on ni vertices. Some stronger versions of this property were introduced, namely the ones of being online arbitrarily partitionable and recursively arbitrarily partitionable (OL-AP and R-AP for short, respectively), in which the subgraphs induced by a partition...

Connected domatic number in planar graphs

Bert L. Hartnell, Douglas F. Rall (2001)

Czechoslovak Mathematical Journal


A dominating set in a graph G is a connected dominating set of G if it induces a connected subgraph of G . The connected domatic number of G is the maximum number of pairwise disjoint, connected dominating sets in V ( G ) . We establish a sharp lower bound on the number of edges in a connected graph with a given order and given connected domatic number. We also show that a planar graph has connected domatic number at most 4 and give a characterization of planar graphs having connected domatic...