Orthogonal representations of Steiner triple system incidence graphs

DOI10.1016/j.disc.2017.07.009zbMath1370.05024arXiv1708.07741OpenAlexW2744423832MaRDI QIDQ2404398

Louis Deaett, H. Tracy Hall

Publication date: 18 September 2017

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.07741

zbMATH Keywords

Steiner triple systemminimum rank problemminimum semidefinite rankHeawood graphfaithful orthogonal representation

Mathematics Subject Classification ID

Orthogonal arrays, Latin squares, Room squares (05B15) Triple systems (05B07) Graph theory (05C99)

Uses Software

• GitHub
• Minimum Rank

Cites Work

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• Linear algebraic methods in communication complexity
• Vector representations of graphs
• The minimum semidefinite rank of a triangle-free graph
• Zero forcing parameters and minimum rank problems
• Orthogonal vector coloring
• Lower bounds in minimum rank problems
• Sets of vectors with many orthogonal pairs
• Graphs whose positive semi-definite matrices have nullity at most two
• Positive semidefinite zero forcing
• Zero forcing sets and the minimum rank of graphs
• Unitary matrix digraphs and minimum semidefinite rank
• On the minimum semidefinite rank of a simple graph
• On the Minimum Rank Among Positive Semidefinite Matrices with a Given Graph
• On the Shannon capacity of a graph
• The Steiner triple systems of order 19
• Parameters Related to Tree‐Width, Zero Forcing, and Maximum Nullity of a Graph
• Kochen–Specker Sets and the Rank-1 Quantum Chromatic Number

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