A lower estimate for the achromatic number of irreducible graphs |
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Authors: | Attila Máté |
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Affiliation: | Department of Mathematics, Brooklyn College (CUNY), Bedford Avenue and Avenue H, Brooklyn, New York 11210, USA |
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Abstract: | The achromatic number of a graph is the largest number of independent sets its vertex set can be split into in such a way that the union of any two of these sets is not independent. A graph is irreducible if no two vertices have the same neighborhood. The achromatic number of an irreducible graph with n vertices is shown to be while an example of Erdös shows that it need not be log n/log 2+2 for any n. The proof uses an indiscernibility argument. |
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