Fixed Point Property for Finite Ordered Sets that Contain No Crowns with 6 or More Elements
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We prove that, for a finite ordered set P that contains no crowns with 6 or more elements, it can be determined in polynomial time if P has the fixed point property. This result is obtained by proving that every such ordered set must contain a point of rank 1 that has a unique lower cover or a retractable minimal element.
KeywordsOrdered set Fixed point property Crown Irreducible point Retractable point d2-collapsible Dimension 2
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The author thanks the referees for constructive suggestions that improved and streamlined the presentation.