Geodesic
On stratification and domination in graphs
Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 2, pp. 249-272

Voir la notice de l'article provenant de la source Library of Science

A graph G is 2-stratified if its vertex set is partitioned into two classes (each of which is a stratum or a color class), where the vertices in one class are colored red and those in the other class are colored blue. Let F be a 2-stratified graph rooted at some blue vertex v. An F-coloring of a graph is a red-blue coloring of the vertices of G in which every blue vertex v belongs to a copy of F rooted at v. The F-domination number γ_F(G) is the minimum number of red vertices in an F-coloring of G. In this paper, we study F-domination, where F is a 2-stratified red-blue-blue path of order 3 rooted at a blue end-vertex. We present characterizations of connected graphs of order n with F-domination number n or 1 and establish several realization results on F-domination number and other domination parameters.
Keywords: stratified graph, F-domination, domination 
@article{DMGT_2006_26_2_a6,
     author = {Gera, Ralucca and Zhang, Ping},
     title = {On stratification and domination in graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {249--272},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2006_26_2_a6/}
}
TY  - JOUR
AU  - Gera, Ralucca
AU  - Zhang, Ping
TI  - On stratification and domination in graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2006
SP  - 249
EP  - 272
VL  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2006_26_2_a6/
LA  - en
ID  - DMGT_2006_26_2_a6
ER  - 
%0 Journal Article
%A Gera, Ralucca
%A Zhang, Ping
%T On stratification and domination in graphs
%J Discussiones Mathematicae. Graph Theory
%D 2006
%P 249-272
%V 26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2006_26_2_a6/
%G en
%F DMGT_2006_26_2_a6
Gera, Ralucca; Zhang, Ping. On stratification and domination in graphs. Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 2, pp. 249-272. http://geodesic.mathdoc.fr/item/DMGT_2006_26_2_a6/