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Koch FINAL 04 25 2023 with cert.pdf (423.31 KB)

ETD Abstract Container

Abstract Header

Applying Computational Resources to the Down-Arrow Problem

Koch, Johnathan
http://orcid.org/0009-0002-6093-9768
http://rave.ohiolink.edu/etdc/view?acc_num=ysu1682511073109112

Abstract Details

2023, Master of Science in Mathematics, Youngstown State University, Department of Mathematics and Statistics.
A graph G is said to arrow a graph H if every red-blue edge coloring of G presents a monochromatic H, and is written G→H. The down-arrow Ramsey set reports all subgraphs H of a graph G for which G→H. Formally, the down-arrow Ramsey set is a graph G is ↓G:= {H⊆G: G→H }. Calculating this set by way of scientific computing is computationally prohibitive with the resources commonly available to graph theorists and other academics. Using existing research into complete graphs, the down-arrow Ramsey sets for small complete graphs (Kn for 2 ≤ n ≤ 7) can be generated quickly. For larger complete graphs (Kn for 8 ≤ n ≤ 11) specific pre-processing steps are leveraged to speed up calculations in addition to existing data sets. Presented is work on the development of a Python script to generate the down-arrow Ramsey set of a graph through efficient memory management and parallel computing methodologies. The down-arrow generator is used to report new results on complete graphs as well as complete bipartite graphs, and assorted other graphs.
Alexis Byers, PhD (Advisor)
Alina Lazar, PhD (Committee Member)
Anita O'Mellan, PhD (Committee Member)
46 p.
Computer Science; Mathematics
Graph theory; Ramsey theory; Edge-coloring; Graph methods; Scientific computing; Python; Parallel computing

Recommended Citations

Citations

  • Koch, J. (2023). Applying Computational Resources to the Down-Arrow Problem [Master's thesis, Youngstown State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1682511073109112

    APA Style (7th edition)

  • Koch, Johnathan. Applying Computational Resources to the Down-Arrow Problem. 2023. Youngstown State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ysu1682511073109112.

    MLA Style (8th edition)

  • Koch, Johnathan. "Applying Computational Resources to the Down-Arrow Problem." Master's thesis, Youngstown State University, 2023. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1682511073109112

    Chicago Manual of Style (17th edition)

ysu1682511073109112
166
© 2023, all rights reserved.
This open access ETD is published by Youngstown State University and OhioLINK.
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