Combinatorics and grafs professor-AI-powered combinatorics and graph solver

Example

Calculating chromatic numbers or determining whether a graph is Eulerian or Hamiltonian.

Scenario

A user is working on a problem where they need to prove whether a given graph is Hamiltonian. They can input the graph’s structure and the professor will guide them through the steps required to apply Dirac's theorem or Ore's theorem to determine the Hamiltonian property.

Example

Finding the number of ways to select a subset of nodes with specific properties from a graph or computing the number of derangements in a set.

Scenario

A researcher working on a combinatorial optimization problem asks for help calculating the number of spanning trees in a network graph. The AI could explain Cayley’s formula, show how it applies to the specific graph, and detail the process of enumeration.

Example

Providing detailed explanations of the Erdős-Stone theorem or the Szemerédi regularity lemma.

Scenario

A student preparing for an advanced exam in combinatorics requests an explanation of the Szemerédi regularity lemma, particularly its application in extremal graph theory. The AI breaks down the lemma into manageable sections, explains the intuition behind it, and offers examples of its usage in proving properties of large graphs.