On a problem concerning $k$-subdomination numbers of graphs

Zelinka, Bohdan. "On a problem concerning $k$-subdomination numbers of graphs." Czechoslovak Mathematical Journal 53.3 (2003): 627-629. <http://eudml.org/doc/30804>.

@article{Zelinka2003,
abstract = {One of numerical invariants concerning domination in graphs is the $k$-subdomination number $\gamma ^\{-11\}_\{kS\}(G)$ of a graph $G$. A conjecture concerning it was expressed by J. H. Hattingh, namely that for any connected graph $G$ with $n$ vertices and any $k$ with $\frac\{1\}\{2\} n < k \leqq n$ the inequality $\gamma ^\{-11\}_\{kS\}(G) \leqq 2k - n$ holds. This paper presents a simple counterexample which disproves this conjecture. This counterexample is the graph of the three-dimensional cube and $k=5$.},
author = {Zelinka, Bohdan},
journal = {Czechoslovak Mathematical Journal},
keywords = {$k$-subdomination number of a graph; three-dimensional cube graph; -subdomination number of a graph; three-dimensional cube graph},
language = {eng},
number = {3},
pages = {627-629},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a problem concerning $k$-subdomination numbers of graphs},
url = {http://eudml.org/doc/30804},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Zelinka, Bohdan
TI - On a problem concerning $k$-subdomination numbers of graphs
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 3
SP - 627
EP - 629
AB - One of numerical invariants concerning domination in graphs is the $k$-subdomination number $\gamma ^{-11}_{kS}(G)$ of a graph $G$. A conjecture concerning it was expressed by J. H. Hattingh, namely that for any connected graph $G$ with $n$ vertices and any $k$ with $\frac{1}{2} n < k \leqq n$ the inequality $\gamma ^{-11}_{kS}(G) \leqq 2k - n$ holds. This paper presents a simple counterexample which disproves this conjecture. This counterexample is the graph of the three-dimensional cube and $k=5$.
LA - eng
KW - $k$-subdomination number of a graph; three-dimensional cube graph; -subdomination number of a graph; three-dimensional cube graph
UR - http://eudml.org/doc/30804
ER -