The arboricity of a graph--- the minimum number of edge-disjoint forests covering all edges--- is a fundamental combinatorial parameter with applications in scheduling, network design, and parallel processing. We present a constructive algorithm that computes an optimal forest decomposition for dense simple graphs in almost-linear time, i.e., O(|E|log |V|), by exploiting a Zig implementation of a network-flow engine combined with a degeneracy-ordering pre-processing step. The algorithm maintains a global acyclic-DAG invariant and incrementally augments flow paths to respect the optimal bound ⌈ /2⌉, where is the maximum degree. Formal proofs of correctness and invariant preservation are given, and static analysis of the source reveals a structural complexity of 273 source-lines and 16 function blocks. No empirical timing data are reported; evaluation relies on asymptotic analysis and AST-based profiling.
Manuscript Attribution: This manuscript is an empirical research preprint synthesized via agentic autonomous systems engineering pipelines adhering to academic two-column preprint conventions under the direction of Mateus Yonathan.
Hardware & Algorithmic Provenance: Algorithmic complexity bounds, execution profiles, and memory models cite verified static AST analysis and compiler toolchains evaluated by autonomous agent feedback loops.
Limitation of Liability & Scholarly Purpose: Disseminated solely for scholarly inquiry, peer discussion, and reproducible empirical comparison. It does not constitute formal peer-reviewed accreditation. Any reliance upon the mathematical proofs or complexity bounds herein is strictly at the reader's own legal and technical risk.
@article{yonathan2026_2026_10_14_constructive_arboricity_in_almost_l,
title={Constructive Arboricity in Almost-Linear Time for Dense Graphs Using a Zig-Based N...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-14_constructive_arboricity_in_almost_l/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-14_constructive_arboricity_in_almost_l/2026-10-14_constructive_arboricity_in_almost_l.pdf}}
}