The crossing number of a graph
is the minimum number of edge crossings over all drawings of
in the plane. The main aim of the paper is to give the crossing number of join product
for the wheel
on six vertices, where
is the path on
vertices. Staš and Valiska conjectured that the crossing number of
is equal to
, for all
,
, where Zarankiewicz’s number is defined as
for
. Recently, this conjecture was proved for
by Klešč and Schrötter, and for
by Sta\v s and Valiska. We establish the validity of this conjecture for
. The conjecture also holds due to some isomorphisms for
,
by Klešč, and for
by Staš for all
.
On the crossing number of the join of the wheel on six vertices with a path
Berežný, Štefan and Staš, Michal
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Additional Information
Author(s) | Staš, Michal, Berežný, Štefan |
---|---|
DOI | https://doi.org/10.37193/CJM.2022.02.06 |