Diskretnyi Analiz i Issledovanie Operatsii
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Diskretn. Anal. Issled. Oper.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Diskretnyi Analiz i Issledovanie Operatsii, 2010, Volume 17, Issue 2, Pages 20–38 (Mi da603)  
This article is cited in 12 scientific papers (total in 12 papers)

Acyclic 4-colorability of planar graphs without 4- and 5-cycles

O. V. Borodinab

a S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (310 kB) Citations (12)
References:
PDF
HTML
Abstract: Every planar graph is known to be acyclically 5-colorable (Borodin, 1976). Some sufficient conditions are also obtained for a planar graph to be acyclically 4- and 3-colorable. In particular, the acyclic 4-colorability was proved for the following planar graphs: without 3-, and 4-cycles (Borodin, Kostochka, Woodall, 1999), without 4-, 5- and 6-cycles, without 4-, 5- and 7-cycles, and with neither 4- or 5-cycles nor intersecting 3-cycles (Montassier, Raspaud and Wang, 2006), and also without cycles of length 4, 5 and 8 (Chen, Raspaud, 2009).
In this paper it is proved that each planar graph without 4-cycles and 5-cycles is acyclically 4-colorable. Bibl. 23.
Keywords: planar graphs, acyclic coloring, forbidden cycles.
Received: 17.06.2009
Revised: 11.02.2010
English version:
Journal of Applied and Industrial Mathematics, 2011, Volume 5, Issue 1, Pages 31–43
DOI: https://doi.org/10.1134/S1990478911010042
Bibliographic databases:
Document Type: Article
UDC: 519.17
Language: Russian
Citation: O. V. Borodin, “Acyclic 4-colorability of planar graphs without 4- and 5-cycles”, Diskretn. Anal. Issled. Oper., 17:2 (2010), 20–38; J. Appl. Industr. Math., 5:1 (2011), 31–43
Citation in format AMSBIB
\Bibitem{Bor10}
\by O.~V.~Borodin
\paper Acyclic 4-colorability of planar graphs without 4- and 5-cycles
\jour Diskretn. Anal. Issled. Oper.
\yr 2010
\vol 17
\issue 2
\pages 20--38
\mathnet{http://mi.mathnet.ru/da603}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2682087}
\zmath{https://zbmath.org/?q=an:1249.05109}
\transl
\jour J. Appl. Industr. Math.
\yr 2011
\vol 5
\issue 1
\pages 31--43
\crossref{https://doi.org/10.1134/S1990478911010042}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952358120}
Linking options:
  • https://www.mathnet.ru/eng/da603
  • https://www.mathnet.ru/eng/da/v17/i2/p20
    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Дискретный анализ и исследование операций
    Statistics & downloads:
    Abstract page:455
    Full-text PDF :106
    References:60
    First page:7
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024