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A Complete Characterization Of Near Outer-Planar Graphs, Tanya Allen Lueder Genannt Luehr Nov 2018

A Complete Characterization Of Near Outer-Planar Graphs, Tanya Allen Lueder Genannt Luehr

Doctoral Dissertations

A graph is outer-planar (OP) if it has a plane embedding in which all of the vertices lie on the boundary of the outer face. A graph is near outer-planar (NOP) if it is edgeless or has an edge whose deletion results in an outer-planar graph. An edge of a non outer-planar graph whose removal results in an outer-planar graph is a vulnerable edge. This dissertation focuses on near outer-planar (NOP) graphs. We describe the class of all such graphs in terms of a finite list of excluded graphs, in a manner similar to the well-known Kuratowski Theorem for planar …


Investigating The Parent Functions: African-American Families And Schools Collaborating To Improve Secondary Mathematics Achievement, Frank E. Staples Jr. Mar 2018

Investigating The Parent Functions: African-American Families And Schools Collaborating To Improve Secondary Mathematics Achievement, Frank E. Staples Jr.

Doctoral Dissertations

The purpose of this study was to identify and evaluate specific strategies that encouraged school personnel and African-American family members to collaborate in a spirit of mutual respect to promote and support student learning and development in high school mathematics. Three research questions were used to (a) determine if strategies identified by the participants were effective or non-effective, (b) determine if there were any similarities or differences with respect to how family members and school personnel think about or assess specific strategies, and (c) assess the results of implemented strategies. This goal was accomplished by (1) convening a group of …