New almost-planar crossing-critical graph families

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F07%3A00024653" target="_blank" >RIV/00216224:14330/07:00024653 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
New almost-planar crossing-critical graph families
Original language description
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 $5$ in crossing-critical graphs remains open. Furthermore, our 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 $big[4,6-frac8{k+1}big)$.
Czech name
Nove temer planarni prusecikove kriticke grafy
Czech description
Konstuhujeme k-prusecikove kriticke grafy obsahujici libovolne mnoho vrcholu kazdeho sudeho stupne.

Project
<a href="/en/project/GA201%2F05%2F0050" target="_blank" >GA201/05/0050: Structural properties and algorithmic complexity of discrete problems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2007
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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