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A366728
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2-tone chromatic number of the square of a cycle with n vertices.
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1
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6, 8, 10, 9, 7, 8, 8, 8, 8, 7, 8, 7, 7, 7, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7
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OFFSET
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3,1
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COMMENTS
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The 2-tone chromatic number of a graph G is the smallest number of colors for which G has a coloring where every vertex has two distinct colors, no adjacent vertices have a common color, and no pair of vertices at distance 2 have two common colors.
The square of a cycle is formed by adding edges between all vertices at distance 2 in the cycle.
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LINKS
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FORMULA
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a(n) = 7 for all n>17.
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EXAMPLE
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The colorings for (broken) cycles with orders 7 through 13 are shown below.
-12-34-56-71-23-45-67-
-12-34-56-78-13-24-57-68-
-12-34-56-17-23-45-16-37-58-
-12-34-56-71-23-68-15-24-38-57-
-12-34-56-17-24-36-58-14-26-38-57-
-12-34-56-71-32-54-16-37-52-14-36-57-
-12-34-56-71-32-54-16-37-58-14-32-57-68-
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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