Turán’s Graph Theorem and Maximum Independent Sets in Brandt Semigroups
نویسنده
چکیده
Let Bn be an aperiodic Brandt semigroup M0[G;n, n;P ] where G is the trivial group, n ∈ N and P = (aij)n×n with aij = 1G if i = j and aij = 0 otherwise. The maximum size of an independent set in Bn is known to be bn2/4c+n, where bn2/4c denotes the largest integer not greater than n2/4. We reprove this result using Turán’s famous graph theorem. Moreover, we give a characterization of all independent sets in Bn with size bn2/4c+ n.
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