Graduation Year


Date of Thesis Acceptance

Spring 5-11-2016

Major Department or Program



Barry Balof


This thesis considers the open problem in topological graph theory: What is the largest connected graph of minimum degree 3 which has everywhere positive combinatorial curvature but is not in one of the infinite families of graphs of positive combinatorial curvature? This problem involves the generalization of the notion of curvature (a geometric concept) to graphs (a combinatorial structure). The thesis presents past progress on the upper and lower bounds for this problem as well as graph operations that may be used in the future for improving the lower bound.

Page Count


Subject Headings

Surfaces -- Mathematical models, Combinatorial geometry, Euler characteristic, Combinatorial designs and configurations, Theorie & Analyse -- topographical graph, Whitman College -- Dissertation collection 2016 -- Mathematics Department

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Document Type

Public Accessible Thesis

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Mathematics Commons



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