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تسجيل مستخدم جديدLarge Simple d-Cycles in Simplicial Complexes
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We show that the size of the largest simple d-cycle in a simplicial d-complex $K$ is at least a square root of $K$s density. This generalizes a well-known classical result of ErdH{o}s and Gallai cite{EG59} for graphs. We use methods from matroid theory applied to combinatorial simplicial complexes.
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