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Reinforcement learning for graph theory, II. Small Ramsey numbers

Mohammad Ghebleh, Salem Al-Yakoob, Ali Kanso, Dragan Stevanović

Abstract

We describe here how the recent Wagner's approach for applying reinforcement learning to construct examples in graph theory can be used in the search for critical graphs for small Ramsey numbers. We illustrate this application by providing lower bounds for the small Ramsey numbers $R(K_{2,5}, K_{3,5})$, $R(B_3, B_6)$ and $R(B_4, B_5)$ and by improving the lower known bound for $R(W_5, W_7)$.

Reinforcement learning for graph theory, II. Small Ramsey numbers

Abstract

We describe here how the recent Wagner's approach for applying reinforcement learning to construct examples in graph theory can be used in the search for critical graphs for small Ramsey numbers. We illustrate this application by providing lower bounds for the small Ramsey numbers , and and by improving the lower known bound for .
Paper Structure (4 sections, 4 theorems, 4 equations)

This paper contains 4 sections, 4 theorems, 4 equations.

Table of Contents

  1. Introduction
  2. Cross-entropy method for small Ramsey numbers
  3. New lower bounds for Ramsey numbers
  4. Concluding remarks

Key Result

Theorem 3.1

$R(W_5, W_7)\geq 14$.

Theorems & Definitions (8)

  • Theorem 3.1
  • proof
  • Theorem 3.2
  • proof
  • Theorem 3.3
  • proof
  • Theorem 3.4
  • proof