Closed 2-cell embeddings of 5-crosscap embeddable graphs (Q1357273)

The strong embedding conjecture states that every 2-connected graph has a closed 2-cell embedding in some surface, i.e. an embedding in a compact, closed 2-manifold in which the boundary of each face is a circuit in the graph. A graph is called 5-crosscap embeddable if it can be embedded in the surface of non-oriented genus 5. The main result of the paper states that any 2-connected graph which is 5-crosscap embeddable has a closed 2-cell embedding in some surface. As a corollary, it is shown that each such graph has a cycle double cover, i.e. a set of circuits in the graph such that each edge is contained in exactly two of these circuits.