Geodesic
More results on r-inflated graphs: Arboricity, thickness, chromatic number and fractional chromatic number
Ars Mathematica Contemporanea, Tome 4 (2011) no. 1, pp. 5-24.

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The r-inflation of a graph G is the lexicographic product G with Kr. A graph is said to have thickness t if its edges can be partitioned into t sets, each of which induces a planar graph, and t is smallest possible. In the setting of the r-inflation of planar graphs, we investigate the generalization of Ringel's famous Earth-Moon problem: What is the largest chromatic number of any thickness-t graph? In particular, we study classes of planar graphs for which we can determine both the thickness and chromatic number of their 2-inflations, and provide bounds on these parameters for their r-inflations. Moreover, in the same setting, we investigate arboricity and fractional chromatic number as well. We end with a list of open questions.
DOI : 10.26493/1855-3974.175.b78
Keywords: r-inflation, thickness, chromatic number, fractional chromatic number, arboricity 
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Michael O. Albertson; Debra L. Boutin; Ellen Gethner. More results on r-inflated graphs: Arboricity, thickness, chromatic number and fractional chromatic number. Ars Mathematica Contemporanea, Tome 4 (2011) no. 1, pp. 5-24. doi : 10.26493/1855-3974.175.b78. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.175.b78/

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