Connected odd dominating sets in graphs

Yair Caro, William F. Klostermeyer, Raphael Yuster-Yaron

Research output: Contribution to journalArticlepeer-review


An odd dominating set of a simple, undirected graph G = (V, E) is
a set of vertices D ⊆ V such that |N[v] ∩ D| ≡ 1 mod 2 for all vertices
v ∈ V . It is known that every graph has an odd dominating set. In
this paper we consider the concept of connected odd dominating sets.
We prove that the problem of deciding if a graph has a connected odd
dominating set is NP-complete. We also determine the existence or
non-existence of such sets in several classes of graphs. Among other
results, we prove there are only 15 grid graphs that have a connected
odd dominating set.
Original languageEnglish
Pages (from-to)225–239
JournalDiscussiones Mathematicae - Graph Theory
StatePublished - 2005


Dive into the research topics of 'Connected odd dominating sets in graphs'. Together they form a unique fingerprint.

Cite this