The longest uncrossed knight's path refers to a path traced by a knight on a chessboard where the knight visits each square without revisiting any square (i.e., without crossing over itself or visiting the same square more than once). This kind of problem is often explored in the context of graph theory and combinatorial optimization.

by The New Republic

In graph theory, a **matching** is a set of edges in a graph such that no two edges share a common vertex. In other words, it is a way of pairing the vertices of a graph such that each vertex is included in at most one edge of the matching. Here's a more detailed explanation: 1. **Vertices and Edges**: A graph consists of a set of vertices (nodes) and a set of edges (connections between pairs of vertices).

The Maximum Cut (Max Cut) problem is a well-known problem in combinatorial optimization and graph theory. It involves a given undirected graph, where the goal is to partition the set of vertices into two disjoint subsets in such a way that the number of edges between the two subsets is maximized.

The maximum flow problem is a classic optimization problem in network flow theory, which aims to find the maximum flow that can be sent from a source node (often referred to as the "source") to a sink node (often referred to as the "sink" or "target") in a flow network. A flow network is a directed graph where each edge has a capacity representing the maximum allowable flow that can pass through that edge.

The Lavoisier Medal is an award given by the Société Chimique de France (SCF) in recognition of outstanding contributions to the field of chemistry. Named after Antoine Lavoisier, a prominent French chemist often referred to as the "father of modern chemistry," the medal honors individuals who have made significant advancements in chemical research, education, or applications.

The Multi-trials technique is often associated with experimental and statistical research methodologies, particularly in the context of optimization and quality control. Although the term can be used in different fields, it generally refers to the practice of conducting multiple trials or experimental runs to obtain reliable and generalizable results. Here are some key aspects: 1. **Purpose**: The main aim is to understand variability, optimize processes, or improve the reliability of data.

Nondeterministic Constraint Logic (NCL) is a computational framework that combines aspects of constraint satisfaction problems (CSPs) and nondeterministic computation. In traditional constraint logic, one deals with variables, domains, and constraints to find assignments that satisfy certain conditions. Nondeterministic computation, on the other hand, allows for multiple potential outcomes or paths in solving a problem, often represented in theoretical computer science by concepts such as nondeterministic Turing machines.

Pebble motion problems are typically mathematical or computational problems that involve simulating the movement of "pebbles" (or similar abstract objects) on a grid or within a defined space, based on specific rules. These problems often appear in areas like combinatorial optimization, game theory, or computer science, particularly in relation to graph theory or dynamic programming.

A polygon is a 2-dimensional polytope, polyhedra is a 3-dimensional polytope.

In the context of linear algebra and vector spaces, a cyclic vector is a vector that generates a cyclic subspace under the action of a linear operator.

The "planted clique" problem is a well-known computational problem in the field of theoretical computer science, particularly in the study of random graphs and computational complexity. It is often used as a benchmark problem for assessing the performance of algorithms designed for detection and clustering in graphs.

The Steiner tree problem is an optimization problem in combinatorial optimization and graph theory. It involves finding the minimum-weight subgraph that connects a given set of points (called terminals) in a weighted graph. This subgraph may include additional points (called Steiner points) that are not in the original set of terminals, and these points can help reduce the overall length of the connecting tree.