For positive integers $n\ge r$, let $\lambda(r,n)$ denote the \emph{maximal relative projection constant} of $r$-dimensional subspaces of $\ell_\infty^n$ and $\lambda(r)$ denote the \emph{maximal absolute projection constant}, respectively. It is known that for any fixed $r$, $\lambda(r,n)$ is a non-decreasing sequence...
Hitesh Kumar, Bojan Mohar, S. A. Mojallal et al.· 0 citations
An eigenvalue of a signed graph is called \emph{main} if there exists a corresponding eigenvector non-orthogonal to the all-ones vector. An important result of O'Rourke and Touri (2016) states that almost all (unsigned) graphs have all main eigenvalues. Akbari, Fran\c{c}a, Ghasemian, Javarsineh, and de Lima (2021) cons...
S. Akbari, Hitesh Kumar, Bojan Mohar et al.· 1 citation
For a simple graph $G$ of order $n$, let $\lambda_1(G)\ge \cdots \ge \lambda_n(G)$ denote its adjacency eigenvalues. Hong's problem asks for the optimal upper bound for $\lambda_k(G)$. A recent theorem of Sivashankar gives, for every $k\ge3$, \[ \lambda_k(G)\le \frac{(k-2)\sqrt{k+1}+2}{2k(k-1)}\,n-1, \] with sharp exam...
Hitesh Kumar, Bojan Mohar, S. A. Mojallal et al.· 0 citations
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