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4 papers · 2 filters
The Generation of All Regular Rational Orthogonal Matrices
Quanyu Tang, Wei Wang, Hao Zhang
A \emph{rational orthogonal matrix} is an orthogonal matrix with rational entries, and is called \emph{regular} if each of its row sum equals one, i.e., where …
Spectral supersaturation: Triangles and bowties
Yongtao Li, Lihua Feng, Yuejian Peng
Recently, Ning and Zhai (2023) proved that every -vertex graph with has at least triangles, unless $G=K_{\lcei…
A spectral Erdős-Rademacher theorem
Yongtao Li, Lu Lu, Yuejian Peng
A classical result of Erdős and Rademacher (1955) indicates a supersaturation phenomenon. It says that if is a graph on vertices with at least $\lfloor {n^2}/{4} \rfloor +1…
A spectral Erdős-Faudree-Rousseau theorem
Yongtao Li, Lihua Feng, Yuejian Peng
A well-known theorem of Mantel states that every -vertex graph with more than edges contains a triangle. An interesting problem in extremal graph theory…