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Creators/Authors contains: "Dhawan, Abhishek"

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  1. ; (, Proceedings of the American Mathematical Society)
    We show that every Borel graph G G of subexponential growth has a Borel proper edge-coloring with Δ<#comment/> ( G ) + 1 \Delta (G) + 1 colors. We deduce this from a stronger result, namely that an n n -vertex (finite) graph G G of subexponential growth can be properly edge-colored using Δ<#comment/> ( G ) + 1 \Delta (G) + 1 colors by an O ( log ∗<#comment/> ⁡<#comment/> n ) O(\log ^\ast n) -round deterministic distributed algorithm in theLOCALmodel, where the implied constants in the O ( ⋅<#comment/> ) O(\cdot ) notation are determined by a bound on the growth rate of G G . 
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    Free, publicly-accessible full text available January 1, 2026
  2. ; ; (, Proceedings of Thirty Sixth Conference on Learning Theory)
    Accepted Manuscript Full Text Available
  3. ; ; (, Proceedings of Thirty Sixth Conference on Learning Theory)
    We consider a symmetric mixture of linear regressions with random samples from the pairwise comparison design, which can be seen as a noisy version of a type of Euclidean distance geometry problem. We analyze the expectation-maximization (EM) algorithm locally around the ground truth and establish that the sequence converges linearly, providing an $$\ell_\infty$$-norm guarantee on the estimation error of the iterates. Furthermore, we show that the limit of the EM sequence achieves the sharp rate of estimation in the $$\ell_2$$-norm, matching the information-theoretically optimal constant. We also argue through simulation that convergence from a random initialization is much more delicate in this setting, and does not appear to occur in general. Our results show that the EM algorithm can exhibit several unique behaviors when the covariate distribution is suitably structured. 
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    Accepted Manuscript Full Text Available
  4. ; ; (, Combinatorics, Probability and Computing)
    Abstract A conjecture of Alon, Krivelevich and Sudakov states that, for any graph $$F$$ , there is a constant $$c_F \gt 0$$ such that if $$G$$ is an $$F$$ -free graph of maximum degree $$\Delta$$ , then $$\chi\!(G) \leqslant c_F \Delta/ \log\!\Delta$$ . Alon, Krivelevich and Sudakov verified this conjecture for a class of graphs $$F$$ that includes all bipartite graphs. Moreover, it follows from recent work by Davies, Kang, Pirot and Sereni that if $$G$$ is $$K_{t,t}$$ -free, then $$\chi\!(G) \leqslant (t + o(1)) \Delta/ \log\!\Delta$$ as $$\Delta \to \infty$$ . We improve this bound to $$(1+o(1)) \Delta/\log\!\Delta$$ , making the constant factor independent of $$t$$ . We further extend our result to the DP-colouring setting (also known as correspondence colouring), introduced by Dvořák and Postle. 
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