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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1276,
author = {Yair Caro and William F. Klostermeyer and Raphael Yuster},
title = {Connected odd dominating sets in graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {25},
year = {2005},
pages = {225-239},
zbl = {1103.05058},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1276}
}
Yair Caro; William F. Klostermeyer; Raphael Yuster. Connected odd dominating sets in graphs. Discussiones Mathematicae Graph Theory, Tome 25 (2005) pp. 225-239. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1276/
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