TY - JOUR
T1 - Surface Embedding of Non-Bipartite $k$-Extendable Graphs
AU - Lu , Hongliang
AU - Wang , David G. L.
JO - Annals of Applied Mathematics
VL - 1
SP - 1
EP - 24
PY - 2022
DA - 2022/01
SN - 38
DO - http://doi.org/10.4208/aam.OA-2021-0008
UR - https://global-sci.org/intro/article_detail/aam/20171.html
KW - Non-bipartite graph, matching extension, surface embedding.
AB - <p style="text-align: justify;">For every surface, we find the minimum number $k$ such that every non-bipartite graph that is embeddable in that surface is not $k$-extendable. In particular, we construct a family of $3$-extendable graphs which we call bow-tie graphs. This confirms the existence of an infinite number of $3$-extendable non-bipartite graphs that are&nbsp; embeddable in the Klein bottle.</p>