Surface embedding of non-bipartite $k$-extendable graphs

Abstract

We find the minimum number $k={\mu }^{\prime }(\Sigma )$ for any surface $\Sigma$, such that every $\Sigma$-embeddable non-bipartite graph is not $k$-extendable. In particular, we construct the so-called bow-tie graphs $C_6\bowtie P_n$, and show that they are $3$-extendable. This confirms the existence of an infinite number of $3$-extendable non-bipartite graphs which can be embedded in the Klein bottle.

17 pages, 5 figures

References in corpus (1)

• Surface embedding of $(n,k)$-extendable graphs