Applied Math · Mathematics & Statistics
Combinatorics
The newest papers in Combinatorics that ReadSearch has read, newest first. Each links to its own page, with its authors, date, where it was published and the original.
228 papers, from 31 August 2026 to 5 November 2026: 168 arXiv preprints and 60 OpenAlex records.
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Newest papers, page 9
Spanning Trees with Many Leaves in Graphs of Minimum Degree at Least 7
We give a polynomial-time algorithm that constructs, in every connected $n$-vertex graph of minimum degree at least $7$, a spanning tree with at least $\frac{25200}{46189}n>0.5455\,n$ leaves.Construction of Partial Join Graphs with Perfect State Transfer in Shunt Decomposition-Based Quantum Walks
In this paper, we define directed partial join graphs with signed couplings and construct discrete-time quantum-walk transition operators for these graphs using the shunt-decomposition framework.Duality for matrix space questions
We present a new proof of a classical theorem of Dieudonné: if a linear space of $n\times n$ matrices consists entirely of singular matrices, then its dimension is at most $n^2-n$.Minimal representations of topology-preserving quantum-like states
We provide an equitable partition that gives an exact, minimal representation for the graph Cartesian product formed from quantum-like bits that preserves the relevant spectral and topological…Sampling Line-Graph Colorings with Constant Extra Colors
Let $G$ be the line graph of a finite simple graph, with $n\geq1$ vertices and maximum degree $Δ$.A 27 x 27 x 27 counterexample to Comon's conjecture
We report an explicit construction of a 27 x 27 x 27 symmetric tensor with rational entries that has tensor rank 55 over the rational numbers and symmetric tensor rank 56 over the complex numbers…Biplanar graphs with independence number two are 9-colorable
A graph is biplanar if it is the union of two planar graphs on the same vertex set.A New Upper Bound for the Turán Density of the Tetrahedron
We prove that the Turán density of the tetrahedron $K_4^{(3)}$ satisfies $π(K_4^{(3)}) \le 14993367693127837/26880000000000000 < 0.557789$, improving Baber's upper bound of $0.5615$ and closing…Clique-dependent strongly sublinear treewidth and strongly sublinear tree-independence number
We establish a strongly sublinear counterpart of a recent result of Chudnovsky, E S, and Lokshtanov (arXiv 2025) on treewidth and tree-independence number.Dual-GNN Multilevel Coarsening for Maximum Independent Set
The maximum independent set (MIS) problem is a fundamental NP-hard combinatorial optimization problem with applications in scheduling, resource allocation, and network analysis.PermuFormer: Multi-Task Pretraining for Permutation Representation in Algebraic Combinatorics
Diverse pretraining has been shown to be an effective method for learning reusable, domain-aware representations that provide a starting point for fine-tuning on downstream tasks.The Mirror Theorem: Central Incidence Saturation in Keith Recurrences
Can a mirror emerge when numbers return?Inverse Baer deformations and finite simple skew braces of nilpotent type
Finite simple skew braces with non-abelian additive group remain largely unexplored.Vector Balancing in Polynomial Time
We present a spectral signing algorithm solving the Komlós problem with a constant discrepancy in polynomial time.A general counting and sampling Lovász local lemma
Consider a constraint satisfaction problem $\mathbf{C}$ on finitely many independent random variables with dependency graph $G$.Kadison--Singer partitions and Bilu--Linial graph signings in polynomial time
We prove two main algorithmic results in spectral discrepancy.Stable Regularity Lemmas: Efficient Algorithms and Essentially Tight Littlestone Bounds
In this paper, we determine the precise asymptotics of the number of parts of stable regularity equipartitions in terms of the Littlestone dimension: every graph $G$ of Littlestone dimension…More (shifted) runners, less loneliness
The shifted lonely runner conjecture was recently disproved by Blanco, Criado and Santos.A two-step supercongruence for an Apéry-like sequence
Let $G_n=\sum_{k=0}^n4^k\binom{2n-2k}{n-k}^{2}\binom{2k}{k}$.A cyclic non-Ramsey heptagon
We present a construction with seven points on a circle that is not Ramsey, disproving a conjecture of Erdős, Graham, Montgomery, Rothschild, Spencer and Straus.