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1. Hunt, Alexis. Establishing a Connection Between Graph Structure, Logic, and Language Theory.

Degree: 2015, University of Waterloo

URL: http://hdl.handle.net/10012/9648

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.

Subjects/Keywords: 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

…graphs will be quite important, as the basis later for the *HR* *algebra*:
Definition 3.17. An s… …JS
JSt
Set of all finite graphs with sources in N
Sorted *algebra* of graphs with sources… …all models of φ
Quotient *algebra* of M
Monadic second-order logic of all RG formulas
30
17… …x28;M)
P α (S)
Powerset *algebra* of M
Generalized powerset of S
14
5
r(… …x29;
STRpres
*Algebra* of relational signatures
Collection of all R-structures
Quasi-domain…

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APA (6^{th} Edition):

Hunt, A. (2015). Establishing a Connection Between Graph Structure, Logic, and Language Theory. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/9648

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Hunt, Alexis. “Establishing a Connection Between Graph Structure, Logic, and Language Theory.” 2015. Thesis, University of Waterloo. Accessed July 03, 2020. http://hdl.handle.net/10012/9648.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Hunt, Alexis. “Establishing a Connection Between Graph Structure, Logic, and Language Theory.” 2015. Web. 03 Jul 2020.

Vancouver:

Hunt A. Establishing a Connection Between Graph Structure, Logic, and Language Theory. [Internet] [Thesis]. University of Waterloo; 2015. [cited 2020 Jul 03]. Available from: http://hdl.handle.net/10012/9648.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Hunt A. Establishing a Connection Between Graph Structure, Logic, and Language Theory. [Thesis]. University of Waterloo; 2015. Available from: http://hdl.handle.net/10012/9648

Not specified: Masters Thesis or Doctoral Dissertation