English

A Chrome extension that turns any OpenStreetMap view into a directed graph — exportable as JSON, GraphML, CSV, or LaTeX TikZ.

From LP to IP: why integrality matters, LP relaxations, and why rounding fails.

Branch and bound: the workhorse algorithm for integer programming, explained with a complete knapsack example.

Cutting planes and branch-and-cut: tightening LP relaxations and how modern solvers solve integer programs.

An introduction to linear programming: definitions, standard form, geometric intuition, and practical examples.

The simplex method explained: slack variables, tableaux, pivoting, degeneracy, and a complete worked example.

Duality in linear programming: the dual problem, strong duality, complementary slackness, shadow prices, and sensitivity analysis.

Construction and improvement heuristics for the TSP: nearest neighbor, greedy, 2-opt, 3-opt, and Or-opt.

Metaheuristics for the TSP: simulated annealing, genetic algorithms, and ant colony optimization.

Applications of minimum-cost flows and series conclusion

Minimum-cost flows

Applications of maximum flow

Ford-Fulkerson and Edmonds-Karp

Residual graphs and the Max-Flow Min-Cut Theorem

Definitions and first properties

We computationally verify Gallai's Path Decomposition Conjecture for all connected graphs with up to 11 vertices, processing over one billion graphs using preprocessing, greedy heuristics, and an ILP solver.

Matchings

Graph coloring

Directed graphs

A brief introduction to the Traveling Salesperson Problem (TSP)

Trees and their properties

Walks, paths, and connectivity

Basic definitions and first observations and examples

Some graph classes

Start of the network flow series

Birth of Graph Theory

In this short article I want to write down the needed steps in order to generate a list of all graphs (no automorphisms!) with nauty.