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Published in:
Graph Modification Problems: A Modern Perspective Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Union Closed Tree Convex Sets

Authors : Tian Liu, Ke Xu

Published in: Frontiers in Algorithmics

Publisher: Springer International Publishing

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Abstract

We show that the union closed sets conjecture holds for tree convex sets. The union closed sets conjecture says that in every union closed set system, there is an element to appear in at least half of the members of the system. In tree convex set systems, there is a tree on the elements such that each subset induces a subtree. Our proof relies on the well known Helly property of hypertrees and an equivalent graph formulation of the union closed sets conjecture given in (Bruhn, H., Charbit, P. and Telle, J.A.: The graph formulation of the union-closed sets conjecture. Proc. of EuroComb 2013, 73–78 (2013)).

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Metadata
Title
Union Closed Tree Convex Sets
Authors
Tian Liu
Ke Xu
Copyright Year
2015
Book
Frontiers in Algorithmics

Print ISBN: 978-3-319-19646-6

Electronic ISBN: 978-3-319-19647-3

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-19647-3_19

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