An easy counting argument shows that if G is overfull then
If G is not overfull
but it
contains an
overfull
subgraph H with
Not every
Class 2
Not every Class 2 graph necessarily contains an overfull subgraph with the same maximum degree
The smallest one is P
the graph
obtained
from the Petersen graph
by removing an
arbitrary
For all known of these graphs
vertex
Petersen
graph