A graph is an apex graph if it contains a vertex whose deletion leaves a planar graph. The family of apex graphs is minor-closed and so it is characterized by a finite list of minor-minimal non-members. The long-standing problem of determining this finite list of apex obstructions remains open. This paper determines the $133$ minor-minimal, non-apex graphs that have connectivity two.
@article{10_37236_8382,
author = {Adam S. Jobson and Andr\'e E. K\'ezdy},
title = {All minor-minimal apex obstructions with connectivity two},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {1},
doi = {10.37236/8382},
zbl = {1456.05040},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8382/}
}
TY - JOUR
AU - Adam S. Jobson
AU - André E. Kézdy
TI - All minor-minimal apex obstructions with connectivity two
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/8382/
DO - 10.37236/8382
ID - 10_37236_8382
ER -
%0 Journal Article
%A Adam S. Jobson
%A André E. Kézdy
%T All minor-minimal apex obstructions with connectivity two
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/8382/
%R 10.37236/8382
%F 10_37236_8382
Adam S. Jobson; André E. Kézdy. All minor-minimal apex obstructions with connectivity two. The electronic journal of combinatorics, Tome 28 (2021) no. 1. doi: 10.37236/8382
