Stars and Bonds in Crossing-Critical Graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F10%3A00045366" target="_blank" >RIV/00216224:14330/10:00045366 - 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
Stars and Bonds in Crossing-Critical Graphs
Original language description
The structure of all known infinite families of crossing--critical graphs has led to the conjecture that crossing--critical graphs have bounded bandwidth. If true, this would imply that crossing--critical graphs have bounded degree, that is, that they cannot contain subdivisions of $K_{1,n}$ for arbitrarily large $n$. In this paper we prove two results that revolve around this conjecture. On the positive side, we show that crossing--critical graphs cannot contain subdivisions of $K_{2,n}$ for arbitrarily large $n$. On the negative side, we show that there are graphs with arbitrarily large maximum degree that are $2$-crossing--critical in the projective plane.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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