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On acyclic colorings of direct products

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Špacapan S., Horvat A.

Discussiones Mathematicae Graph Theory

2008

tom 28

nr 2

323-333

A coloring of a graph G is an acyclic coloring if the union of any two color classes induces a forest. It is proved that the acyclic chromatic number of direct product of two trees T₁ and T₂ equals min{Δ(T₁) + 1, Δ(T₂) + 1}. We also prove that the acyclic chromatic number of direct product of two complete graphs Kₘ and Kₙ is mn-m-2, where m ≥ n ≥ 4. Several bounds for the acyclic chromatic number of direct products are given and in connection to this some questions are raised.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Horvat A.

1 Špacapan S.

1 2008

Wyniki wyszukiwania

On acyclic colorings of direct products