The maximum density of a no-three-in-line set on the checkerboard is at most the middle real root α of the cubic equation 401α³ - 1744α² + 2240α - 768 = 0.
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The winner of the normal partizan domination game is determined for complete split graphs including star forests under arbitrary initial colorings.
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No-three-in-line sets on the checkerboard grid
The maximum density of a no-three-in-line set on the checkerboard is at most the middle real root α of the cubic equation 401α³ - 1744α² + 2240α - 768 = 0.
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The Normal Domination Partizan Game in Stars
The winner of the normal partizan domination game is determined for complete split graphs including star forests under arbitrary initial colorings.