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A Study of Abstract Elementary Classes in the context of Graphs

Navaneetha Madaparambu Rajan

TL;DR

This work analyzes several properties of Forb(G) and versions of ForB-Con( G) in the context of aecs and presents some examples of classes of graphs which contradicts amalgamation property.

Abstract

In the framework of graphs, we study abstract elementary classes (aecs). In this work we analyze several properties of Forb(G) and versions of Forb-Con(G) in the context of aecs and we present some examples of classes of graphs which contradicts amalgamation property.

A Study of Abstract Elementary Classes in the context of Graphs

TL;DR

This work analyzes several properties of Forb(G) and versions of ForB-Con( G) in the context of aecs and presents some examples of classes of graphs which contradicts amalgamation property.

Abstract

In the framework of graphs, we study abstract elementary classes (aecs). In this work we analyze several properties of Forb(G) and versions of Forb-Con(G) in the context of aecs and we present some examples of classes of graphs which contradicts amalgamation property.
Paper Structure (6 sections, 15 theorems, 3 equations)

This paper contains 6 sections, 15 theorems, 3 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Classes of Graphs Contradicting the Amalgamation Property
  4. Forb(G)
  5. Versions of Forb-con(G)
  6. Acknowledgement

Key Result

Proposition 2.5

Let $K^G$ be the class of graphs. The pair $(K^G,\preceq)$ forms an AEC.

Theorems & Definitions (51)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Proposition 2.5
  • proof
  • Proposition 2.6
  • proof
  • Remark 2.7
  • Proposition 2.8
  • ...and 41 more