The crossing number of a projective graph is quadratic in the face-width
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F07%3A00024642" target="_blank" >RIV/00216224:14330/07:00024642 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
The crossing number of a projective graph is quadratic in the face-width
Original language description
We show that for each nonnegative integer $g$ there is a constant $constc > 0$ such that every graph that embeds in the projective plane with face--width at least $r$ has crossing number at least $constc r^2$ in the orientable surface of genus $g$.As a corollary, we give a polynomial time constant factor approximation algorithm for the crossing number of projective graphs with bounded degree.
Czech name
Průsečíkové číslo projektivních grafů je kvadratické ve face-width
Czech description
Dokážeme, že grafy nakreslené v projektivní rovině mají rovinné průsečíkové číslo rostoucí kvadraticky ve své stěnové šířce.
Classification
Type
O - Miscellaneous
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2007
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů