Symmetric Union Closed Families

Fuente: arXiv
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Autor principal: M, Nived J
Formato: Preprint
Publicado: 2024
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author M, Nived J
author_facet M, Nived J
contents We demonstrate that when a graph exhibits a specific type of symmetry, it satisfies the Union Closed Conjecture(UCC). Additionally, we show that certain graph classes, such as Cylindrical Grid Graphs and Torus Grid Graphs also satisfy the conjecture. We prove the known result that the union closed family generated by cyclic translates of a fixed set satisfies the UCC, offering a simpler proof via symmetry arguments. Later, we show that the union closed family generated by the family obtained through cyclically shifting elements from selected translates also satisfies the conjecture.
format Preprint
id arxiv_https___arxiv_org_abs_2411_06588
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Symmetric Union Closed Families
M, Nived J
Combinatorics
05D05 (primary) 05C35, 05C90 (secondary)
We demonstrate that when a graph exhibits a specific type of symmetry, it satisfies the Union Closed Conjecture(UCC). Additionally, we show that certain graph classes, such as Cylindrical Grid Graphs and Torus Grid Graphs also satisfy the conjecture. We prove the known result that the union closed family generated by cyclic translates of a fixed set satisfies the UCC, offering a simpler proof via symmetry arguments. Later, we show that the union closed family generated by the family obtained through cyclically shifting elements from selected translates also satisfies the conjecture.
title Symmetric Union Closed Families
topic Combinatorics
05D05 (primary) 05C35, 05C90 (secondary)
url https://arxiv.org/abs/2411.06588