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.
Get the few papers worth your time in Combinatorics every morning.
Follow Combinatorics and ReadSearch reads its new papers each day, then brings you the few worth reading, each with its key finding in a sentence.
Newest papers, page 3
Latin cubes of order $4$ and $4320$-point quaternionic constructions in ${\mathbb R}^{16}$
Possibly the most enduring lower-bound record for kissing numbers in dimensions greater than $8$ (excluding $24$) is $$ κ_{16}\geq 4320. $$ This lower bound is attained by a shell of the famous…Maximal input entropy for binary two-deletion and two-insertion channels
Under uniform transmission, we determine the received binary words that maximize input entropy for two-deletion and two-insertion channels.On Sparse Graph Limits for Neural Combinatorial Optimization
Graph neural networks are often trained on small graphs and deployed on larger ones, raising the question of which graph information must be preserved for combinatorial optimization values to…The Value of Steiner Hubs in Two-Hop Distance Labeling
Two-hop distance labelings were introduced in 2002 by Cohen, Halperin, Kaplan, and Zwick with hubs of two kinds: vertices of the graph, or, in their Steiner variant, arbitrary objects carrying…Fluid Limits and Upper Bounds for Randomized Greedy Matching
The Modified Randomized Greedy (MRG) algorithm [Tinhofer (1984), Aronson-Dyer-Frieze-Suen (1995)] is a classical greedy algorithm for finding approximate maximum matchings.Quantum Vehicle Routing Problem: a smart initialization strategy for ill-conditioned optimization landscapes
With the expansion of complex transport infrastructure, new paths for linking different destinations have emerged, allowing the definition of multiple routes.Traveling Salesman Problem on Graphs with Proportional Independent Set
We give a deterministic algorithm for minimum-cost Hamiltonian cycle in undirected graphs with arbitrary real edge costs and an independent set of size at least $αn$, for any fixed $3/7<α\le1/2$.On $t$-designs supported by self-orthogonal codes
We study self-orthogonal $t$-$(v,k,λ)$ designs satisfying the condition that the codes generated by the designs are self-orthogonal codes whose codewords of minimum weight $k$ correspond to the…List 3-Coloring in tame classes of graphs in quasipolynomial time
A class of graphs $\mathcal{G}$ is tame if there is a constant c such that every $n$-vertex graph in $\mathcal{G}$ has at most $n^c$ minimal separators.Bethe Hessian Recovery through the Kesten-Stigum Regime
We show that outlier eigenvectors of the Bethe Hessian achieve weak recovery in the stochastic block model down to the Kesten-Stigum threshold, for every fixed common expected degree $d>1$.Revisiting the directed pathwidth of h-semicomplete digraphs
A digraph is $h$-semicomplete if every vertex has at most $h$ non-neighbors.Extremal character spectra of finite projective systems
Let $\mathcal M$ be a finite spanning multiset of points in ${\rm PG}(k-1,q)$, and let ${\rm Char}_{\mathcal M}$ be its character function.Two choices suffice: $k$-out sampling leaves $O(n/k)$ intercomponent edges for $k\geq 2$
Given a simple undirected graph on $n$ vertices, random $k$-out sampling forms a spanning subgraph by having each vertex independently choose $k$ incident edges uniformly with replacement.A Counterexample to the Gyarmati-Matolcsi-Ruzsa Conjecture
We provide a counterexample to the non-abelian Gyarmati-Matolcsi-Ruzsa conjecture.A new upper bound for $A(19,6,8)$
We compute Polak's bound $A_4(19,6,8)$ for binary constant weight codes, obtaining the numerical value $673.04001$.Online carpooling against an oblivious adversary
In the online carpooling problem, edges on $n$ vertices arrive one at a time and must be oriented immediately, so as to keep the difference between the indegree and the outdegree of every vertex…Four-Coloring Planar Graphs in Linear Time
The famous Four Color Theorem (4CT) states that any planar graph can be colored with four colors, but how do we find a 4-coloring?From Trees to Binary Trees: Approximation Algorithms and a PTAS
Kellerhals, Krebs, Nichterlein, and Schmid introduced the optimization problem Tree in Binary Tree (TBT), where, given a tree $T$, the task is to find a binary tree $S^*$ with $V(T)=V(S^*)$ that…Half-Optimal Induced Matchings in Random Graphs: Online and Low-Degree Algorithms
For many optimization problems on random graphs, most prominently the largest independent set problem, natural algorithms reach only half the optimum, and such factor-two gaps are known to be sharp…On the Quantum Chromatic Gap II
We confirm a conjecture of the first author [SODA'26] on a strong form of pseudo-telepathy for Khot's $d$-to-$1$ games: for every $d\geq 4$, every $ε>0$, and every $k\in\mathbb N$, there is a…