Establishing a Connection Between Graph Structure, Logic, and Language Theory

graph structure;logic;formal languages;language theory;monadic second-order logic;tree-decompositions;hyperedge replacement;HR algebra;graph theory;well-quasi-ordering;cone graph;cone ideal;tree-generator;obstruction-width;Combinatorics and Optimization

Hunt, Alexis

University of Waterloo

关键词: graph structure;    logic;    formal languages;    language theory;    monadic second-order logic;    tree-decompositions;    hyperedge replacement;    HR algebra;    graph theory;    well-quasi-ordering;    cone graph;    cone ideal;    tree-generator;    obstruction-width;    Combinatorics and Optimization;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/9648/5/Hunt_Alexis.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

The field of graph structure theory was given life by the Graph Minors Project of Robertson and Seymour, which developed many tools for understanding the way graphs relate to each other and culminated in the proof of the Graph Minors Theorem. One area of ongoing research in the field is attempting to strengthen the Graph Minors Theorem to sets of graphs, and sets of sets of graphs, and so on.At the same time, there is growing interest in the applications of logic and formal languages to graph theory, and a significant amount of work in this field has recently been consolidated in the publication of a book by Courcelle and Engelfriet.We investigate the potential applications of logic and formal languages to the field of graph structure theory, suggesting a new area of research which may provide fruitful.