Bojan Mohar

activity

20242026

collaborators

11 papers

math.CO2026

The switching conjecture for main eigenvalues is asymptotically true

Saieed Akbari, Hitesh Kumar, Bojan Mohar +1

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 (…

math.CO2026

Orthogonal signed graphs of degree 5

Maxwell Levit, Bojan Mohar, Behruz Tayfeh-Rezaie

An orthogonal signed graph is a connected signed graph whose signed adjacency matrix has pairwise orthogonal rows. They are closely related to Hadamard matrices, maximal arrangemen…

math.FA2026

Stability of maximal relative projection constants

Hitesh Kumar, Bojan Mohar, Seyed Ahmad Mojallal +1

For positive integers $n \geq r$ , let $λ (r, n)$ denote the \emph{maximal relative projection constant} of $r$ -dimensional subspaces of $ℓ_{\infty}^{n}$ and $λ (r)$ denote the \emph{maxi…

math.CO2026

Extremal graphs for the $k$ -th eigenvalue

Hitesh Kumar, Bojan Mohar, Seyed Ahmad Mojallal +1

For a simple graph $G$ of order $n$ , let $λ_{1} (G) \geq \dots \geq λ_{n} (G)$ denote its adjacency eigenvalues. Hong's problem asks for the optimal upper bound for $λ_{k} (G)$ . A recent theo…

math.CO2026

An improved bound for the strong clique index of graphs

Hitesh Kumar, Bojan Mohar, Shivaramakrishna Pragada

For a graph $G$ with line graph $L (G)$ , $χ (L (G)^{2})$ and $ω (L (G)^{2})$ are called the \emph{strong chromatic index} and \emph{strong clique index} of $G$ , respectively. A well-known c…

math.CO2026

2-cell embeddings of cubic graphs I. The unstable dual

MacKenzie Carr, Bojan Mohar

In this paper, the first of a two-part series, we explore 2-cell embeddings of cubic graphs, particularly those with small genus. Using local rotations, we introduce a new way of d…

math.CO2026

Convex combination of first and second eigenvalues of trees

Hitesh Kumar, Bojan Mohar, Shivaramakrishna Pragada +1

For a graph $G$ , let $λ_{1} (G)$ and $λ_{2} (G)$ denote the largest and the second largest adjacency eigenvalue of $G$ . The sum $λ_{1} (G) + λ_{2} (G)$ is called the \emph{spectral sum} of $G$ …

math.CO2025

Spectrally symmetric orientations of graphs

Saieed Akbari, Jonathan Aloni, Maxwell Levit +2

The Hermitian adjacency matrices of digraphs based on the sixth root of unity were introduced in [B. Mohar, A new kind of Hermitian matrices for digraphs, Linear Alg. Appl. (2020)]…

math.CO2025

A Counterexample to a Conjecture of Lovász

Alexander Clow, Penny Haxell, Bojan Mohar

In 1975 Lovász conjectured that every $r$ -partite, $r$ -uniform hypergraph contains $r - 1$ vertices whose deletion reduces the matching number. If true, this statement would imply a…

math.CO2025

Refinement of a conjecture on positive square energy of graphs

Saieed Akbari, Hitesh Kumar, Bojan Mohar +2

Let $G$ be a simple graph of order $n$ with eigenvalues $λ_{1} (G) \geq \dots \geq λ_{n} (G)$ . Define \[s^+(G)=\sum_{λ_i >0} λ_i^2(G), \quad s^-(G)=\sum_{λ_i<0} λ_i^2(G).\] It was conjec…

math.CO2024

On the second largest adjacency eigenvalue of trees with given diameter

Hitesh Kumar, Bojan Mohar, Shivaramakrishna Pragada +1

For a graph $G$ , let $λ_{2} (G)$ denote the second largest eigenvalue of the adjacency matrix of $G$ . We determine the extremal trees with maximum/minimum adjacency eigenvalue $λ_{2}$ i…

The switching conjecture for main eigenvalues is asymptotically true

Orthogonal signed graphs of degree 5

Stability of maximal relative projection constants

Extremal graphs for the k-th eigenvalue

An improved bound for the strong clique index of graphs

2-cell embeddings of cubic graphs I. The unstable dual

Convex combination of first and second eigenvalues of trees

Spectrally symmetric orientations of graphs

A Counterexample to a Conjecture of Lovász

Refinement of a conjecture on positive square energy of graphs

On the second largest adjacency eigenvalue of trees with given diameter

Extremal graphs for the $k$ -th eigenvalue