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{\bf Petr Hlin\v en\'y}
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{\bf New Infinite Families of Almost-Planar Crossing-Critical Graphs}
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We show that, for all choices of integers $k>2$ and $m$, there are
simple $3$-connected $k$-crossing-critical graphs containing more
than $m$ vertices of each even degree $\leq2k-2$. This construction
answers one half of a question raised by Bokal, while the other half
asking analogously about vertices of odd degrees at least $7$ in
crossing-critical graphs remains open. Furthermore, our newly
constructed graphs have several other interesting properties; for
instance, they are almost planar and their average degree can attain
any rational value in the interval
$\big[3+{1\over5},6-{8\over k+1}\big)$.
\bye