Geodesic
The well-covered dimension of products of graphs
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 4, pp. 811-827.

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

We discuss how to find the well-covered dimension of a graph that is the Cartesian product of paths, cycles, complete graphs, and other simple graphs. Also, a bound for the well-covered dimension of K_n × G is found, provided that G has a largest greedy independent decomposition of length c lt; n. Formulae to find the well-covered dimension of graphs obtained by vertex blowups on a known graph, and to the lexicographic product of two known graphs are also given.
Keywords: well-covered dimension, maximal independent sets 
@article{DMGT_2014_34_4_a10,
     author = {Birnbaum, Isaac and Kuneli, Megan and McDonald, Robyn and Urabe, Katherine and Vega, Oscar},
     title = {The well-covered dimension of products of graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {811--827},
     publisher = {mathdoc},
     volume = {34},
     number = {4},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2014_34_4_a10/}
}
TY  - JOUR
AU  - Birnbaum, Isaac
AU  - Kuneli, Megan
AU  - McDonald, Robyn
AU  - Urabe, Katherine
AU  - Vega, Oscar
TI  - The well-covered dimension of products of graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2014
SP  - 811
EP  - 827
VL  - 34
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2014_34_4_a10/
LA  - en
ID  - DMGT_2014_34_4_a10
ER  - 
%0 Journal Article
%A Birnbaum, Isaac
%A Kuneli, Megan
%A McDonald, Robyn
%A Urabe, Katherine
%A Vega, Oscar
%T The well-covered dimension of products of graphs
%J Discussiones Mathematicae. Graph Theory
%D 2014
%P 811-827
%V 34
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2014_34_4_a10/
%G en
%F DMGT_2014_34_4_a10
Birnbaum, Isaac; Kuneli, Megan; McDonald, Robyn; Urabe, Katherine; Vega, Oscar. The well-covered dimension of products of graphs. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 4, pp. 811-827. http://geodesic.mathdoc.fr/item/DMGT_2014_34_4_a10/

[1] J.I. Brown and R.J. Nowakowski, Well-covered vector spaces of graphs, SIAM J. Discrete Math. 19 (2005) 952-965. doi:10.1137/S0895480101393039

[2] Y. Caro, M.N. Ellingham and J.E. Ramey, Local structure when all maximal independent sets have equal weight, SIAM J. Discrete Math. 11 (1998) 644-654. doi:10.1137/S0895480196300479

[3] Y. Caro and R. Yuster, The uniformity space of hypergraphs and its applications, Discrete Math. 202 (1999) 1-19. doi:10.1016/S0012-365X(98)00344-6

[4] A. Ovetsky, On the well-coveredness of Cartesian products of graphs, Discrete Math. 309 (2009) 238-246. doi:10.1016/j.disc.2007.12.083

[5] M.D. Plummer, Some covering concepts in graphs, J. Combin. Theory 8 (1970) 91-98. doi:10.1016/S0021-9800(70)80011-4

[6] D.B. West, Introduction to Graph Theory, Second Edition (Prentice Hall, Upper Saddle River, 2001).