Document Type
Lecture
Publication Date
1-28-2004
Abstract
A closed 2-cell embedding of a graph G in a surface is an embedding such that the closure of each face is homeomorphic to a closed disk. A long-standing conjecture, the Strong Embedding Conjecture, states that every 2-connected graph has a closed 2-cell embedding in some surface. The Strong Embedding Conjecture is closely related to another important conjecture, called the Cycle Double Cover Conjecture, which states that every 2-edge connected graph has a set of cycles such that each edge is contained in exactly two of these cycles. A closed 2-cell embedding of a graph implies the cycle double cover of that graph simply by taking the face boundaries as the set of cycles. In this talk, we discuss the closed 2-cell embeddings in orientable surfaces for graphs embeddable in the projective plane and the torus.
Relational Format
presentation
Recommended Citation
Zha, Xiaoya, "Closed 2-cell Embeddings of Graphs Embeddable in the Projective Plane and the Torus" (2004). Combinatorics Seminar. 106.
https://egrove.olemiss.edu/math_combinatorics/106
