The hottest Graph Theory Substack posts right now

LLM reasoning can be done using graph structures instead of chains or trees.
Graph of Thoughts (GoT) is a framework that represents LLM information as a versatile graph.
LangChain's LangSmith is a debugging and testing tool for LLMs.

k-Core Decomposition is a way to explore the structure of networks by identifying the largest subgraph where every node has a specified minimum degree.
The k-Core Decomposition algorithm involves recursively removing nodes with degrees lower than a specified threshold to reveal the k-core and k-shell structure of a graph.
The degree of a node in a k-core doesn't have an upper limit, providing unique insights into network connectivity beyond traditional degree-based analysis.

A countable random graph is a graph where you flip a coin to decide the edges between vertices in an infinite set, and the result is the same graph almost every time.
Graph theory is a complex subject with beautiful theorems, and different notions of graphs exist, such as directed graphs and simple graphs.
In mathematics, there are variations in graph definitions, such as allowing reflexivity or multiple edges, but in simpler contexts, graphs are typically referred to as simple graphs.

A bridge in a graph is an edge that, if removed, disconnects the graph.
Finding all the bridges in a graph is an important problem in graph theory.
Graph traversal and DFS are commonly used techniques for solving problems related to finding bridges in a graph.

Eulerian tours visit all edges exactly once.
Hamiltonian tours visit all vertices exactly once.
Finding Hamiltonian tours is more complex than finding Eulerian tours, often requiring heuristic algorithms.

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In a graph, a bridge is an edge that makes the graph disconnected when removed.
Bridges are an important concept in graph theory for understanding connectivity.
Understanding how to find all bridges in a graph is crucial for various applications.

Matching problems can be modeled using bipartite graphs where no edges go between vertices of the same type.
In graph theory, a full matching of one partition of a bipartite graph implies that every vertex in that partition has at least as many neighbors in the other partition.
Hall's theorem provides a necessary and sufficient condition for determining the existence of a full matching in a bipartite graph.

Trees in graph theory are hierarchical structures with a root and child relationship.
A tree in graph theory is a connected, acyclic, and undirected graph.
Spanning trees connect all vertices of a graph with the minimum number of edges and can be found using a breadth-first search algorithm.

Identifying bridges in a graph is crucial to understanding connectivity.
Creating a brute force solution involves removing edges and checking for graph connectedness.
Optimal solutions for graph problems often involve tracking reachable vertices.

The problem involves finding all bridges in a graph, where removing an edge disconnects the graph.
This specific problem was asked by Mozilla in a coding interview scenario.
Access to solutions and more problems is offered through subscriptions to the publication.