found a counterexample
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		@@ -6,3 +6,12 @@ n=7 , m=10      graph gap = 1          projection gap = 2         factor=2
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[1 0 0 1 0 0 1 0 0 0 1]
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[0 1 0 0 1 0 0 1 0 0 1]
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[0 0 1 0 0 1 0 0 1 1 1]
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n=8 , m=14      graph gap = 1          projection gap = 15/7      factor=15/7       max=2.1428571428571432
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[1 1 1 0 0 0 0 0 0 0 0 0 0 0 1]
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[0 0 0 1 1 1 0 0 0 0 0 0 0 0 1]
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[0 0 0 0 0 0 1 1 1 0 0 0 0 0 1]
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[0 0 0 0 0 0 0 0 0 1 1 1 0 0 1]
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[0 0 0 0 0 0 0 0 0 0 0 0 1 1 1]
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[1 0 0 1 0 0 1 0 0 1 0 0 0 0 1]
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[0 1 0 0 1 0 0 1 0 0 1 0 1 0 1]
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[0 0 1 0 0 1 0 0 1 0 0 1 0 1 1]
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