Extremal problems for cycles in graphs and hypergraphs

cycles, paths, Berge cycles, Berge paths, Turan problems, hypergraphs, extremal combinatorics, graph theory, hypergraph theory

Luo, Ruth

关键词: cycles, paths, Berge cycles, Berge paths, Turan problems, hypergraphs, extremal combinatorics, graph theory, hypergraph theory;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/105633/LUO-DISSERTATION-2019.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

In this thesis, we study several generalizations of Turan type problems in graphs and hypergraphs. In particular, we focus on graphs and hypergraphs without long cycles or long paths, extending famous results of Erdos and Gallai. Results include bounds on the size of such objects as well as stability theorems about the structure of extremal and almost extremal objects.