6,101 research outputs found
On building 4-critical plane and projective plane multiwheels from odd wheels
We build unbounded classes of plane and projective plane multiwheels that are
4-critical that are received summing odd wheels as edge sums modulo two. These
classes can be considered as ascending from single common graph that can be
received as edge sum modulo two of the octahedron graph O and the minimal wheel
W3. All graphs of these classes belong to 2n-2-edges-class of graphs, among
which are those that quadrangulate projective plane, i.e., graphs from
Gr\"otzsch class, received applying Mycielski's Construction to odd cycle.Comment: 10 page
A tight Erd\H{o}s-P\'osa function for wheel minors
Let denote the wheel on vertices. We prove that for every integer
there is a constant such that for every integer
and every graph , either has vertex-disjoint subgraphs each
containing as minor, or there is a subset of at most
vertices such that has no minor. This is best possible, up to the
value of . We conjecture that the result remains true more generally if we
replace with any fixed planar graph .Comment: 15 pages, 1 figur
- …