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Fall coloring of graphs I

100%

Balakrishnan R., Kavaskar T.

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 3

385-391

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Balakrishnan R.

1 Kavaskar T.

1 2010

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Fall coloring of graphs I