# The Well-Covered Dimension Of Products Of Graphs

Isaac Birnbaum; Megan Kuneli; Robyn McDonald; Katherine Urabe; Oscar Vega

Discussiones Mathematicae Graph Theory (2014)

- Volume: 34, Issue: 4, page 811-827
- ISSN: 2083-5892

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top## Abstract

top## How to cite

topIsaac Birnbaum, et al. "The Well-Covered Dimension Of Products Of Graphs." Discussiones Mathematicae Graph Theory 34.4 (2014): 811-827. <http://eudml.org/doc/269828>.

@article{IsaacBirnbaum2014,

abstract = {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 Kn × G is found, provided that G has a largest greedy independent decomposition of length c < 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.},

author = {Isaac Birnbaum, Megan Kuneli, Robyn McDonald, Katherine Urabe, Oscar Vega},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {well-covered dimension; maximal independent sets.; maximal independent sets},

language = {eng},

number = {4},

pages = {811-827},

title = {The Well-Covered Dimension Of Products Of Graphs},

url = {http://eudml.org/doc/269828},

volume = {34},

year = {2014},

}

TY - JOUR

AU - Isaac Birnbaum

AU - Megan Kuneli

AU - Robyn McDonald

AU - Katherine Urabe

AU - Oscar Vega

TI - The Well-Covered Dimension Of Products Of Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2014

VL - 34

IS - 4

SP - 811

EP - 827

AB - 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 Kn × G is found, provided that G has a largest greedy independent decomposition of length c < 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.

LA - eng

KW - well-covered dimension; maximal independent sets.; maximal independent sets

UR - http://eudml.org/doc/269828

ER -

## References

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- [2] Y. Caro, M.N. Ellingham and J.E. Ramey, Local structure when all maximal inde- pendent sets have equal weight , SIAM J. Discrete Math. 11 (1998) 644-654. doi:10.1137/S0895480196300479 Zbl0914.05061
- [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 Zbl0932.05069
- [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 Zbl1229.05239
- [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).

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