惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

G
Google Developers Blog
Apple Machine Learning Research
Apple Machine Learning Research
小众软件
小众软件
Recent Announcements
Recent Announcements
阮一峰的网络日志
阮一峰的网络日志
IT之家
IT之家
A
About on SuperTechFans
量子位
Engineering at Meta
Engineering at Meta
B
Blog
The Cloudflare Blog
博客园 - 【当耐特】
Hugging Face - Blog
Hugging Face - Blog
Y
Y Combinator Blog
J
Java Code Geeks
D
DataBreaches.Net
aimingoo的专栏
aimingoo的专栏
T
Tailwind CSS Blog
H
Help Net Security
钛媒体:引领未来商业与生活新知
钛媒体:引领未来商业与生活新知
V
V2EX
Stack Overflow Blog
Stack Overflow Blog
C
Check Point Blog
酷 壳 – CoolShell
酷 壳 – CoolShell

math updates on arXiv.org

Coupling-Robust Accuracy in Multiphysics Physics Informed Neural Networks via Kronecker-Preconditioned Optimization Non-normal spectral signatures of instability in neural network training dynamics Optimization of randomized neural networks for transfer operator approximation Selective Ambulance Dispatch Under Contextual Travel-Time Uncertainty LLAMA LIMA: A Living Meta-Analysis on the Effects of Generative AI on Learning Mathematics Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations LLMs as Noisy Channels: A Shannon Perspective on Model Capacity and Scaling Laws On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacy Training-Free Looped Transformers Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer Entrywise Error Bounds for Spectral Ranking with Semi-Random Adversaries Asymmetric Scaling Laws from Sparse Features Is Dimensionality a Barrier for Retrieval Models? RA-DCA: A Randomized Active-Set DCA for Directional Stationarity in Max-Structured DC Programs Commutator-Induced Uncertainty in VAEs Weisfeiler-Leman Is Incomplete on Simple Spectrum Graphs, so Canonicalize Them Sparse In-Network Learning via Shortest-Path Backpropagation and Finite-Rate Gating Instance-Optimal Estimation with Multiple LLM Judges on a Budget Entropy Equivalence Testing Expand More, Shrink Less: Shaping Effective-Rank Dynamics for Dense Scaling in Recommendation Any-Dimensional Invariant Universality Operationalizing Individual Fairness via Gradient Descent and Bradley-Terry Models Anytime Training with Schedule-Free Spectral Optimization Diffusion-based Denoising Beats Vanilla Score Matching in Parameter Estimation: A Theoretical Explanation Resilience Characterization of AI-Native Wireless Receivers via Persistent Homology The General Theory of Localization Methods Group-Algebraic Tensors: Provably-optimal Equivariant Learning and Physical Symmetry Discovery General Lower Bounds for Differentially Private Federated Learning with Arbitrary Public-Transcript Interactions PilotWiMAE: Pilot-Native Representation Learning for Wireless Channels Proximal basin hopping: global optimization with guarantees
Every signed planar graph is $5$-choosable: A short proof...
Pie Desire Ebode Atangana, Maxwell Ndognkon Manga · 2026-05-20 · via math updates on arXiv.org

A \emph{signed graph} is a pair $\Gs$ in which $G$ is a finite simple graph and $σ:\E(G)\to\{+1,-1\}$ is a \emph{signature}. Following Máčajová--Raspaud- Škoviera and Jin--Kang--Steffen, a \emph{proper coloring} of $\Gs$ is a map $c:\V(G)\to\Z$ with $c(u)\neσ(uv)\,c(v)$ for every edge $uv$, and $\Gs$ is \emph{signed $k$-choosable} if such a coloring exists from any list assignment $L$ with $|L(v)|\ge k$. In a celebrated two-page note, Thomassen proved that every planar graph is $5$ choosable, and Jin, Kang, and Steffen subsequently extended this to signed planar graphs. Our principal contribution is a short, self-contained, and \emph{signature-blind} proof of the latter: the inductive bookkeeping inserts one factor of $σ(\cdot)$ uniformly into every constraint, so that with $σ\equiv +1$ the argument reduces verbatim to Thomassen's original. From the strengthened extension statement (\cref{thm:main}) we deduce the main result (\cref{thm:JKS}: $\chs\Gs\le 5$ for every planar signed graph), the Máčajová--Raspaud--Škoviera signed Five-Color Theorem in the symmetric palette $\Ns{2}=\{-2,-1,0,1,2\}$, the Switching Invariance Lemma, $3$-choosability of outerplanar signed graphs, $1$-defective signed $4$-choosability of planar signed graphs, a sandwich inequality relating $\chs$ to the unsigned and positive'' choice numbers, and a polynomial-time list-coloring algorithm. Voigt's planar non-$4$-choosable graph and Mirzakhani's smaller variant show the bound $5$ is best possible. We close with examples illustrating that negative edges genuinely refine unsigned phenomena, a comparison table situating our work in the literature, and several open problems.