Published in Preprint, 2026
We show that the graph family $D^\prime(k,q)$ contains 10-cycles for every $k\ge 2$ and $q=3^n$, $n\ge 2$.
Recommended citation: Sayan Mukherjee. "The bipartite graphs $D^\prime(k,q)$ have low girth." Preprint, 12 pages. https://sayan.mukherjee.moe/files/DprimekqLowGirth.pdf
Published in ACM Transactions on Graphics (SIGGRAPH 2026), 2026
A framework for lifting image-space stylizations into path-space and applications in line and tone rendering.
Recommended citation: Rex West, Sayan Mukherjee and Yonghao Yue. "Lifting Lines and Tone: Image-space Stylization in Path-space." ACM Trans. Graph. 45, 4, Article 138 (July 2026), 15 pages. https://doi.org/10.1145/3811359
Published in arXiv Preprint, 2025
We use eigenvalues of the graph laplacian to prove bounds on vertex congestion.
Recommended citation: Mukherjee, Sayan and Akiyama, Shinichiro. "Congestion bounds via Laplacian eigenvalues and their application to tensor networks with arbitrary geometry." arXiv Preprint arXiv:2510.02725 https://arxiv.org/abs/2510.02725
Published in arXiv Preprint, 2025
We modify the power iteration method to achieve locally differentially private clustering for general graphs with constant privacy budget.
Recommended citation: Suppakitpaisarn, Vorapong and Mukherjee, Sayan. "Locally Differentially Private Graph Clustering via the Power Iteration Method." arXiv Preprint arXiv:2505.11169 https://arxiv.org/abs/2505.11169
Published in ACM Transactions on Graphics (SIGGRAPH 2024), 2024
A step towards integrating non-photorealistic stylizations into physically-based rendering systems.
Recommended citation: Rex West and Sayan Mukherjee. "Stylized Rendering as a Function of Expectation." ACM Trans. Graph. 43, 4, Article 96 (July 2024), 19 pages. https://doi.org/10.1145/3658161
Published in European Journal of Combinatorics Vol. 118, May 2024, 103935, 2024
Turan numbers for hypergraph suspensions.
Recommended citation: Mukherjee, Sayan. "Extremal Numbers of Hypergraph Suspensions of Even Cycles." European Journal of Combinatorics Volume 118, May 2024, 103935. https://doi.org/10.1016/j.ejc.2024.103935
Published in Discrete Mathematics Vol. 347 (4), 2024
Counting number of triangles in graphs forbidding suspensions of the path on 4 vertices.
Recommended citation: Mukherjee, Sayan. "Exact generalized Turan number for $K_3$ versus suspension of $P_4$". Discrete Mathematics 347 (4) https://doi.org/10.1016/j.disc.2023.113866
Published in Transactions on Machine Learning Research, May 2025, 2023
Spectral clustering is robust for social networks in general with privacy budget $\epsilon=O(\log n)$, and this result is tight.
Recommended citation: Mukherjee, Sayan and Suppakitpaisarn, Vorapong. "Local Differential Privacy-Preserving Spectral Clustering for General Graphs." Transactions on Machine Learning Research (TMLR), May 2025 https://arxiv.org/abs/2309.06867
Published in Discrete Mathematics Vol. 346 (6), 2023
Counting number of triangles in graphs forbidding suspensions of bipartite graphs.
Recommended citation: Mubayi, Dhruv, and Mukherjee, Sayan. "Triangles in graphs without bipartite suspensions." Discrete Mathematics 346 (6). https://doi.org/10.1016/j.disc.2023.113355
Published in European Journal of Combinatorics Vol. 110, 2022
Stability theorems for some Kruskal-Katona type results.
Recommended citation: Liu, Xizhi and Mukherjee, Sayan. "Stability theorems for some Kruskal-Katona type results." European J. Comb. 110 (2023) arXiv:2006.04848 (2020). https://doi.org/10.1016/j.ejc.2022.103666
Published in Conference on Learning Theory 2022, 2022
Tight query complexity bounds for learning graph partitions.
Recommended citation: Liu, Xizhi, and Mukherjee, Sayan. "Tight query complexity bounds for learning graph partitions." 35th Conference on Learning Theory (COLT). Proceedings in Machine Learning Research (2022). https://arxiv.org/pdf/2112.07897.pdf
Published in IEEE Transactions on Quantum Engineering, 2022
We analyze the list coloring problem and demonstrate a fast quantum algorithm for it.
Recommended citation: Mukherjee, Sayan. "A Grover search-based algorithm for the list coloring problem." IEEE Transactions on Quantum Engineering Volume 3 (2022). https://doi.org/10.1109/TQE.2022.3151137
Published in Computer Graphics Forum; Pacific Graphics Conference 2021, 2021
Using neural networks to perform sequence transformation.
Recommended citation: Mukherjee, Sabyasachi; Mukherjee, Sayan; Hua, Binh-Son; Umetani, Nobuyuki and Meister, Daniel. "Neural Sequence Transformation." Computer Graphics Forum (Wiley), Volume 40, Issue 7, Pages 131-140 (2021). https://doi.org/10.1111/cgf.14407
Published in University of Illinois at Chicago, 2021
Ph.D. Thesis for Ph.D. in Mathematics defended at University of Illinois at Chicago.
Recommended citation: Mukherjee, Sayan. "Extremal Problems for Graphs and Hypergraphs." Thesis,Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago (2021). https://doi.org/10.25417/UIC.17026274.V1
Published in Journal of Combinatorics, 2021
Maximum subgraphs without hypergraph families.
Recommended citation: Mubayi, Dhruv and Mukherjee, Sayan. "Maximum H-free subgraphs." Journal of Combinatorics Volume 12 (2) Pages 185-214 (2021). https://doi.org/10.4310/JOC.2021.v12.n2.a1
Published in Sādhanā, 2019
Maximum subgraphs without hypergraph families.
Recommended citation: Mukherjee, Sayan; Ghosh, Debraj and De, Rajat K. "Expected return time to the initial state for biochemical systems with linear cyclic chains: unidirectional and bidirectional reactions." Sādhanā (Springer India) Volume 44, Issue 1, Pages 1-12 (2019). https://doi.org/10.1007/s12046-018-0989-5
Published in Journal of Classical Geometry, 2013
Neuberg Locus and its properties.
Recommended citation: Banerjee, Debdyuti and Mukherjee, Sayan. "Neuberg Locus And Its Properties." Journal of Classical Geometry, Volume 2 (26) (2013).