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Cairncross-HonorsPaper.pdf (323.85 KB)
ETD Abstract Container
Abstract Header
Proper 3-colorings of cycles and hypercubes
Author Info
Cairncross, Emily
ORCID® Identifier
http://orcid.org/0000-0002-3821-1183
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1621606265779497
Abstract Details
Year and Degree
2021, BA, Oberlin College, Mathematics.
Abstract
In this paper, we look at two families of graphs, cycles and hypercubes, and compare how their sets of proper 3-colorings differ as the graphs get arbitrarily large. In particular, we find the probability of pairs of vertices at various distances being the same color in order to understand the range and scale of interactions between them. As we look at larger and larger cycles, larger and larger hypercubes, patterns begin to emerge. While the colors of vertices fixed fractions of the cycle away from each other are independent, a random 3-coloring of the hypercube is essentially a 2-coloring. This models how local constraints can propagate very differently through different kinds of networks.
Committee
Elizabeth L. Wilmer (Advisor)
Pages
22 p.
Subject Headings
Mathematics
Keywords
Hypercubes
;
Graphs
;
Cycles
;
Models
;
Color
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Citations
Cairncross, E. (2021).
Proper 3-colorings of cycles and hypercubes
[Undergraduate thesis, Oberlin College]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1621606265779497
APA Style (7th edition)
Cairncross, Emily.
Proper 3-colorings of cycles and hypercubes.
2021. Oberlin College, Undergraduate thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1621606265779497.
MLA Style (8th edition)
Cairncross, Emily. "Proper 3-colorings of cycles and hypercubes." Undergraduate thesis, Oberlin College, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1621606265779497
Chicago Manual of Style (17th edition)
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Document number:
oberlin1621606265779497
Download Count:
658
Copyright Info
© 2021, all rights reserved.
This open access ETD is published by Oberlin College Honors Theses and OhioLINK.