#### Presentation Title

#### Faculty Sponsor

Dr. Daniela Genova

#### Faculty Sponsor College

College of Arts and Sciences

#### Faculty Sponsor Department

Mathematics & Statistics

#### Location

SOARS Virtual Conference

#### Presentation Website

https://unfsoars.domains.unf.edu/embedding-graphs-on-surfaces-and-graph-minors/

#### Keywords

SOARS (Conference) (2020 : University of North Florida) -- Posters; University of North Florida. Office of Undergraduate Research; University of North Florida. Graduate School; College students – Research -- Florida – Jacksonville -- Posters; University of North Florida – Undergraduates -- Research -- Posters; University of North Florida. Department of Mathematics and Statistics -- Research -- Posters; Engineering, Math, and Computer Sciences -- Research – Posters

#### Abstract

A planar graph is a graph that can be drawn in such a way in the plane, so that no edges cross each other. In other words, it is a graph that can be embedded in the plane. We discuss the conditions that make a graph embeddable on a sphere with k handles. Then, using vertex deletions and edge contractions, which produce graph minors, we examine if a graph is minimally nonembeddable on a surface. To conclude, we discuss an important result, that the set of minimally nonembeddable graphs on a surface is finite.

#### Included in

Embedding Graphs on Surfaces and Graph Minors

SOARS Virtual Conference

A planar graph is a graph that can be drawn in such a way in the plane, so that no edges cross each other. In other words, it is a graph that can be embedded in the plane. We discuss the conditions that make a graph embeddable on a sphere with k handles. Then, using vertex deletions and edge contractions, which produce graph minors, we examine if a graph is minimally nonembeddable on a surface. To conclude, we discuss an important result, that the set of minimally nonembeddable graphs on a surface is finite.

https://digitalcommons.unf.edu/soars/2020/spring_2020/126