turkmath.org

This lecture is in the field of graph theory and will serve as an introduction to resolvable graph decompositions; graph factorizations. Methods, applications, and different types of graph decompositions, particularly cycle decompositions, will be discussed. Hamilton cycles are particularly popular in the field, and this popularity rises from optimization problems. Main focus of the talk will be on Hamilton cycle decompositions and a relatively new method based on graph homomorphisms and edge-coloring will be introduced. Other types of interesting cycle decomposition problems, namely Oberwolfach Problem and the Hamilton-Waterloo problem, will also be introduced and new results on those problems will be discussed.