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تسجيل مستخدم جديدPartitions versus sets : a case of duality
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تأليف
Laurent Lyaudet
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In a recent paper, Amini et al. introduce a general framework to prove duality theorems between special decompositions and their dual combinatorial object. They thus unify all known ad-hoc proofs in one single theorem. While this unification process is definitely good, their main theorem remains quite technical and does not give a real insight of why some decompositions admit dual objects and why others do not. The goal of this paper is both to generalise a little this framework and to give an enlightening simple proof of its central theorem.
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Motivated by recent computational models for redistricting and detection of gerrymandering, we study the following problem on graph partitions. Given a graph $G$ and an integer $kgeq 1$, a $k$-district map of $G$ is a partition of $V(G)$ into $k$ non
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