Haodong Zhu
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Haodong Zhu has a total of 7 co-authors. Here are the top co-authors by number of shared publications:
- Noela Müller
Department of Mathematics and Computer Science Eindhoven University of Technology P.O. Box 513 5600 MB Eindhoven The Netherlands
2 shared publications - Remco van der Hofstad
Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands
2 shared publications - Arnab Chatterjee
Faculty of Computer Science TU Dortmund Otto-Hahn-Str. 12 44227 Dortmund Germany
1 shared publication - David Gamarnik
Sloan School of Management, Massachusetts Institute of Technology, Cambridge, USA
1 shared publication - Joon Hyung Lee1 shared publication
- Ralph Neininger
Institute for Mathematics Goethe University Frankfurt Germany
1 shared publication
Latest Publications
- Open Access
Minimum Number of Monochromatic Subgraphs of a Random Graph
We consider the problem of minimizing the number of monochromatic subgraphs of a random graph, when each node of the host graph is assigned one of the two colors. Using a recently discovered contiguity between appearance of strictly balanced subgraphs $F$ in a random graph, and random hypergraphs where copies of $F$ are generated independently, we show that the minimum value converges to a limit, when the expected number of copies of $F$ is linear in the number of nodes $|V|$. Furthermore, using the connections with mean field spin glass models, we obtain an asymptotic expression for this limit as the normalized expected number of copies of $F$ and the size of $F$ diverge to infinity.Open AccessMinimum Number of Monochromatic Subgraphs of a Random Graph
We consider the problem of minimizing the number of monochromatic subgraphs of a random graph, when each node of the host graph is assigned one of the two colors. Using a recently discovered contiguity between appearance of strictly balanced subgraphs $F$ in a random graph, and random hypergraphs where copies of $F$ are generated independently, we show that the minimum value converges to a limit, when the expected number of copies of $F$ is linear in the number of nodes $|V|$. Furthermore, using the connections with mean field spin glass models, we obtain an asymptotic expression for this limit as the normalized expected number of copies of $F$ and the size of $F$ diverge to infinity. - Open Access
Asymptotic size of the Karp-Sipser Core in Configuration Model
We study the asymptotic size of the Karp-Sipser core in the configuration model with arbitrary degree distributions. The Karp-Sipser core is the induced subgraph obtained by iteratively removing all leaves and their neighbors through the leaf-removal process, and finally discarding any isolated vertices \cite{BCC}. Our main result establishes the convergence of the Karp-Sipser core size to an explicit fixed-point equation under general degree assumptions.The approach is based on analyzing the corresponding local weak limit of the configuration model - a unimodular Galton-Watson tree and tracing the evolution process of all vertex states under leaf-removal dynamics by use of the working mechanism of an enhanced version of Warning Propagation along with Node Labeling Propagation.
Open AccessAsymptotic size of the Karp-Sipser Core in Configuration Model
We study the asymptotic size of the Karp-Sipser core in the configuration model with arbitrary degree distributions. The Karp-Sipser core is the induced subgraph obtained by iteratively removing all leaves and their neighbors through the leaf-removal process, and finally discarding any isolated vertices \cite{BCC}. Our main result establishes the convergence of the Karp-Sipser core size to an explicit fixed-point equation under general degree assumptions.The approach is based on analyzing the corresponding local weak limit of the configuration model - a unimodular Galton-Watson tree and tracing the evolution process of all vertex states under leaf-removal dynamics by use of the working mechanism of an enhanced version of Warning Propagation along with Node Labeling Propagation.
- Open Access
The asymptotic rank of adjacency matrices of weighted configuration models over arbitrary fields
We study the asymptotic rank of adjacency matrices of a large class of edge-weighted configuration models. Here, the weight of a (multi-)edge can be any fixed non-zero element from an arbitrary field, as long as it is independent of the (multi-)graph. Our main result demonstrates that the asymptotic behavior of the normalized rank of the adjacency matrix neither depends on the fixed edge-weights, nor on which field they are chosen from. Our approach relies on a novel adaptation of the component exploration method of \cite{janson2009new}, which enables the application of combinatorial techniques from \cite{coja2022rank, HofMul25}.
Open AccessThe asymptotic rank of adjacency matrices of weighted configuration models over arbitrary fields
We study the asymptotic rank of adjacency matrices of a large class of edge-weighted configuration models. Here, the weight of a (multi-)edge can be any fixed non-zero element from an arbitrary field, as long as it is independent of the (multi-)graph. Our main result demonstrates that the asymptotic behavior of the normalized rank of the adjacency matrix neither depends on the fixed edge-weights, nor on which field they are chosen from. Our approach relies on a novel adaptation of the component exploration method of \cite{janson2009new}, which enables the application of combinatorial techniques from \cite{coja2022rank, HofMul25}.
- Open Access
Logarithmic typical distances in preferential attachment models
We prove that the typical distances in a preferential attachment model with out-degree $m\geq 2$ and strictly positive fitness parameter are close to $\log_ν{n}$, where $ν$ is the exponential growth parameter of the local limit of the preferential attachment model. The proof relies on a path-counting technique, the first- and second-moment methods, as well as a novel proof of the convergence of the spectral radius of the offspring operator under a certain truncation.Open AccessLogarithmic typical distances in preferential attachment models
We prove that the typical distances in a preferential attachment model with out-degree $m\geq 2$ and strictly positive fitness parameter are close to $\log_ν{n}$, where $ν$ is the exponential growth parameter of the local limit of the preferential attachment model. The proof relies on a path-counting technique, the first- and second-moment methods, as well as a novel proof of the convergence of the spectral radius of the offspring operator under a certain truncation. - Open Access
Random $2$-SAT: The set of atoms of the limiting empirical marginal distribution
We show that the set of atoms of the limiting empirical marginal distribution in the random $2$-SAT model is $\mathbb Q \cap (0,1)$, for all clause-to-variable densities up to the satisfiability threshold. While for densities up to $1/2$, the measure is purely discrete, we additionally establish the existence of a nontrivial continuous part for any density in $(1/2, 1)$. Our proof is based on the construction of a random variable with the correct distribution as the the root marginal of a multi-type Galton-Watson tree, along with a subsequent analysis of the resulting almost sure recursion.Open AccessRandom $2$-SAT: The set of atoms of the limiting empirical marginal distribution
We show that the set of atoms of the limiting empirical marginal distribution in the random $2$-SAT model is $\mathbb Q \cap (0,1)$, for all clause-to-variable densities up to the satisfiability threshold. While for densities up to $1/2$, the measure is purely discrete, we additionally establish the existence of a nontrivial continuous part for any density in $(1/2, 1)$. Our proof is based on the construction of a random variable with the correct distribution as the the root marginal of a multi-type Galton-Watson tree, along with a subsequent analysis of the resulting almost sure recursion.