Overview Statistic: PDF-Downloads (blue) and Frontdoor-Views (gray)

Cutting planes for families implying Frankl's conjecture

epub ahead of print
  • We find previously unknown families of sets which ensure Frankl's conjecture holds for all families that contain them using an algorithmic framework. The conjecture states that for any nonempty finite union-closed (UC) family there exists an element of the ground set in at least half the sets of the considered UC family. Poonen's Theorem characterizes the existence of weights which determine whether a given UC family implies the conjecture for all UC families which contain it. We design a cutting-plane method that computes the explicit weights which satisfy the existence conditions of Poonen's Theorem. This method enables us to answer several open questions regarding structural properties of UC families, including the construction of a counterexample to a conjecture of Morris from 2006.

Export metadata

Additional Services

Share in Twitter Search Google Scholar Statistics - number of accesses to the document
Author:Jonad Pulaj
Document Type:Article
Parent Title (English):Mathematics of Computation
Date of first Publication:2019/07/25
Accept ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.