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Reachability in K-colored tournaments

Description

Let T be a tournament with edges colored with any number of colors. A rainbow triangle is a 3-colored 3-cycle. A monochromatic sink of T is a vertex which can be reached along a monochromatic path by every other vertex of T. In 1982, Sands, Sauer, and Woodrow asked if…

Let T be a tournament with edges colored with any number of colors. A rainbow triangle is a 3-colored 3-cycle. A monochromatic sink of T is a vertex which can be reached along a monochromatic path by every other vertex of T. In 1982, Sands, Sauer, and Woodrow asked if T has no rainbow triangles, then does T have a monochromatic sink? I answer yes in the following five scenarios: when all 4-cycles are monochromatic, all 4-semi-cycles are near-monochromatic, all 5-semi-cycles are near-monochromatic, all back-paths of an ordering of the vertices are vertex disjoint, and for any vertex in an ordering of the vertices, its back edges are all colored the same. I provide conjectures related to these results that ask if the result is also true for larger cycles and semi-cycles. A ruling class is a set of vertices in T so that every other vertex of T can reach a vertex of the ruling class along a monochromatic path. Every tournament contains a ruling class, although the ruling class may have a trivial size of the order of T. Sands, Sauer, and Woodrow asked (again in 1982) about the minimum size of ruling classes in T. In particular, in a 3-colored tournament, must there be a ruling class of size 3? I answer yes when it is required that all 2-colored cycles have an edge xy so that y has a monochromatic path to x. I conjecture that there is a ruling class of size 3 if there are no rainbow triangles in T. Finally, I present the new topic of alpha-step-chromatic sinks along with related results. I show that for certain values of alpha, a tournament is not guaranteed to have an alpha-step-chromatic sink. In fact, similar to the previous results in this thesis, alpha-step-chromatic sinks can only be demonstrated when additional restrictions are put on the coloring of the tournament's edges, such as excluding rainbow triangles. However, when proving the existence of alpha-step-chromatic sinks, it is only necessary to exclude special types of rainbow triangles.

ContributorsBland, Adam K (Author) / Kierstead, Henry A (Thesis advisor) / Czygrinow, Andrzej M (Committee member) / Hurlbert, Glenn H. (Committee member) / Barcelo, Helene (Committee member) / Aen, Arunabha (Committee member) / Arizona State University (Publisher)

Created2011

Earth, Society, and Justice: An Annotated Syllabus for a Political Geology Course Informed by Decolonial, Radical, and Environmental Justice Theories

Description

Geology and its tangential studies, collectively known and referred to in this thesis as geosciences, have been paramount to the transformation and advancement of society, fundamentally changing the way we view, interact and live with the surrounding natural and built environment. It is important to recognize the value and importance…

Geology and its tangential studies, collectively known and referred to in this thesis as geosciences, have been paramount to the transformation and advancement of society, fundamentally changing the way we view, interact and live with the surrounding natural and built environment. It is important to recognize the value and importance of this interdisciplinary scientific field while reconciling its ties to imperial and colonizing extractive systems which have led to harmful and invasive endeavors. This intersection among geosciences, (environmental) justice studies, and decolonization is intended to promote inclusive pedagogical models through just and equitable methodologies and frameworks as to prevent further injustices and promote recognition and healing of old wounds. By utilizing decolonial frameworks and highlighting the voices of peoples from colonized and exploited landscapes, this annotated syllabus tackles the issues previously described while proposing solutions involving place-based education and the recentering of land within geoscience pedagogical models. (abstract)

ContributorsReed, Cameron E (Author) / Richter, Jennifer (Thesis director) / Semken, Steven (Committee member) / School of Earth and Space Exploration (Contributor, Contributor) / School of Sustainability (Contributor) / Barrett, The Honors College (Contributor)

Created2021-05

ABCTL Quality Management Systems: Medical Testing Lab Process Optimization

Description

The ASU COVID-19 testing lab process was developed to operate as the primary testing site for all ASU staff, students, and specified external individuals. Tests are collected at various collection sites, including a walk-in site at the SDFC and various drive-up sites on campus; analysis is conducted on ASU campus…

The ASU COVID-19 testing lab process was developed to operate as the primary testing site for all ASU staff, students, and specified external individuals. Tests are collected at various collection sites, including a walk-in site at the SDFC and various drive-up sites on campus; analysis is conducted on ASU campus and results are distributed virtually to all patients via the Health Services patient portal. The following is a literature review on past implementations of various process improvement techniques and how they can be applied to the ABCTL testing process to achieve laboratory goals. (abstract)