Re: Non-touching hex-triangles

On 3 Mai, 22:33, I wrote:
I came up with this problem today, but perhaps it is already known?

Consider a tiling of the plane with regular hexagons. A _triangle_
means three mutually adjacent hexagons. We will select some triangles
and colour their hexagons black, but none of them must be adjacent;
i.e., each black hexagon will be adjacent to exactly two other black
hexagons. What is the maximal density of black hexagons?

I can prove that 3/7 <= max density <= 16/35. Is the exact value known
or easy to find?

I have improved the bounds to 4/9 <= max density <= 22/49, and I am
tempted to conjecture that the lower bound is optimal. So, has anyone
seen this before?

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J K Haugland
http://home.no.net/zamunda


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