REAL

Minimal Non-C-Perfect Hypergraphs with Circular Symmetry

Czaun, Péter Bence and Pusztai, Pál and Sebők, Levente and Tuza, Zsolt (2023) Minimal Non-C-Perfect Hypergraphs with Circular Symmetry. SYMMETRY (BASEL), 15 (5). ISSN 2073-8994

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Abstract

In this research paper, we study 3-uniform hypergraphs H=(X,E) with circular symmetry. Two parameters are considered: the largest size α(H) of a set S⊂X not containing any edge E∈E, and the maximum number χ¯(H) of colors in a vertex coloring of H such that each E∈E contains two vertices of the same color. The problem considered here is to characterize those H in which the equality χ¯(H′)=α(H′) holds for every induced subhypergraph H′=(X′,E′) of H. A well-known objection against χ¯(H′)=α(H′) is where ∩E∈E′E=1, termed “monostar”. Steps toward a solution to this approach is to investigate the properties of monostar-free structures. All such H are completely identified up to 16 vertices, with the aid of a computer. Most of them can be shown to satisfy χ¯(H)=α(H), and the few exceptions contain one or both of two specific induced subhypergraphs H5⥁, H6⥁ on five and six vertices, respectively, both with χ¯=2 and α=3. Furthermore, a general conjecture is raised for hypergraphs of prime orders.

Item Type: Article
Subjects: Q Science / természettudomány > QA Mathematics / matematika
SWORD Depositor: MTMT SWORD
Depositing User: MTMT SWORD
Date Deposited: 05 Apr 2024 11:16
Last Modified: 05 Apr 2024 11:16
URI: https://real.mtak.hu/id/eprint/191959

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