Fall coloring of graphs I
Discussiones Mathematicae Graph Theory, Tome 30 (2010) no. 3, p. 385.

Voir la notice de l'article dans European Digital Mathematics Library

A fall coloring of a graph G is a proper coloring of the vertex set of G such that every vertex of G is a color dominating vertex in G (that is, it has at least one neighbor in each of the other color classes). The fall coloring number χ f ( G ) of G is the minimum size of a fall color partition of G (when it exists). Trivially, for any graph G, χ ( G ) ≤ χ f ( G ) . In this paper, we show the existence of an infinite family of graphs G with prescribed values for χ(G) and χ f ( G ) . We also obtain the smallest non-fall colorable graphs with a given minimum degree δ and determine their number. These answer two of the questions raised by Dunbar et al.
Classification : 05C15
Mots-clés : fall coloring of graphs, non-fall colorable graphs, color dominating vertex 
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Rangaswami Balakrishnan; T. Kavaskar. Fall coloring of graphs I. Discussiones Mathematicae Graph Theory, Tome 30 (2010) no. 3, p. 385. https://geodesic-test.mathdoc.fr/item/DMGT_2010__30_3_270859/