Year: 2025
Type: article
Abstract: ABSTRACT This paper investigates five kinds of systems of ‐partitions of , including symmetric Bollobás systems, strong Bollobás systems, Bollobás systems, skew Bollobás systems, and weak Bollobás systems. Many known results on variations of Bollobás systems are unified. Especially, we give a negative answer to a conjecture on Bollobás systems of ‐partitions of that was presented by Hegedüs and Frankl (European J. Comb., 120 [2024], 103983). Even though this conjecture does not hold for general Bollobás systems, we show that it holds for strong Bollobás systems of ‐partitions of .
Source: Journal of Combinatorial Designs
DOI: 10.1002/jcd.22007
Authors: Yu Fang, Xiaomiao Wang, Tao Feng
Institutions: Ningbo University, Beijing Jiaotong University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414487864