Embedding graphs into larger graphs: results, methods, and problems

TL;DR

This survey reviews key results, methods, and open problems in extremal graph theory, emphasizing recent breakthroughs and connections to Lovász, highlighting the field's rapid development and significance.

Contribution

It provides a comprehensive overview of important and recent results in extremal graph theory, including new breakthroughs and methodological insights.

Findings

Highlighting recent breakthrough results

Connecting extremal graph theory to Lovász's work

Identifying open problems and future directions

Abstract

Extremal Graph Theory is a very deep and wide area of modern combinatorics. It is very fast developing, and in this long but relatively short survey we select some of those results which either we feel very important in this field or which are new breakthrough results, or which --- for some other reasons --- are very close to us. Some results discussed here got stronger emphasis, since they are connected to Lov\'asz (and sometimes to us).