Explorations of Plane Graphs with No Odd Faces

Authors

Collyn Valentine, Louisiana Tech UniversityFollow

Document Type

Article

Publication Date

Spring 2025

Abstract

In this paper, we will explore the intersection of two classes of graphs which are foundational in graph theory. The class of planar graphs, P, and the class of bipartite graphs, χ2. In particular, we will explore the edge-maximal graphs in the intersection. Excluded minors are well studied, and the two fundamental operations of deletion and contraction have become core to the field. The focus of our work is to consider the operations in reverse – that is, through single-edge extensions and single-edge co-extensions in the class P ∩ χ2, namely those graphs that are planar having chromatic number 2.

Recommended Citation

Valentine, Collyn, "Explorations of Plane Graphs with No Odd Faces" (2025). Mathematics Senior Capstone Papers. 56.
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/56