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Article

Some Problems and Conjectures About Voloshin Triple Systems

Department of Mathematics and Computer Science, University of Catania, 95125 Catania, Italy
Mathematics 2026, 14(1), 42; https://doi.org/10.3390/math14010042
Submission received: 26 November 2025 / Revised: 16 December 2025 / Accepted: 18 December 2025 / Published: 22 December 2025
(This article belongs to the Special Issue New Perspectives of Graph Theory and Combinatorics)

Abstract

In this paper we give a short survey of Voloshin Triple Systems, which are Steiner Triple Systems with a vertex colouring which colour the blocks using exactly two colours. We also provide two conjectures about VTSs obtained by the construction v2v+1, starting from v=3. Finally, we point out some open problems about Steiner Systems S(2,4,v) with a similar vertex colouring, which could provide similar conjectures.
Keywords: hypergraphs; designs; colourings hypergraphs; designs; colourings

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MDPI and ACS Style

Gionfriddo, M. Some Problems and Conjectures About Voloshin Triple Systems. Mathematics 2026, 14, 42. https://doi.org/10.3390/math14010042

AMA Style

Gionfriddo M. Some Problems and Conjectures About Voloshin Triple Systems. Mathematics. 2026; 14(1):42. https://doi.org/10.3390/math14010042

Chicago/Turabian Style

Gionfriddo, Mario. 2026. "Some Problems and Conjectures About Voloshin Triple Systems" Mathematics 14, no. 1: 42. https://doi.org/10.3390/math14010042

APA Style

Gionfriddo, M. (2026). Some Problems and Conjectures About Voloshin Triple Systems. Mathematics, 14(1), 42. https://doi.org/10.3390/math14010042

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