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Izvestiya: Mathematics, 2005, Volume 69, Issue 5, Pages 1025–1033
DOI: https://doi.org/10.1070/IM2005v069n05ABEH002286 (Mi im659) 		 
This article is cited in 26 scientific papers (total in 26 papers)

A proof of Vassiliev's conjecture on the planarity of singular links

V. O. Manturov
English version PDF (167 kB) Citations (26)
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DOI: https://doi.org/10.1070/IM2005v069n05ABEH002286
Abstract: We prove that a finite 4-valent graph with a cross structure at each vertex cannot be embedded in the plane with respect to this structure if and only if there are two cycles without common edges and with precisely one intersection point that is transversal with respect to the cross structure. This leads to an algorithm for recognizing the planarity of such a graph which is quadratic in the number of vertices.
Received: 29.12.2004
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2005, Volume 69, Issue 5, Pages 169–178
DOI: https://doi.org/10.4213/im659
Bibliographic databases:
UDC: 515.16
MSC: 05C10, 57M27, 68Q25
Language: English
Original paper language: Russian
Citation: V. O. Manturov, “A proof of Vassiliev's conjecture on the planarity of singular links”, Izv. RAN. Ser. Mat., 69:5 (2005), 169–178; Izv. Math., 69:5 (2005), 1025–1033
Citation in format AMSBIB
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\pages 169--178
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\transl
\jour Izv. Math.
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  • https://doi.org/10.1070/IM2005v069n05ABEH002286
  • https://www.mathnet.ru/eng/im/v69/i5/p169
    • This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:842
    Russian version PDF:422
    English version PDF:29
    References:67
    First page:2
     
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