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Diskretn. Anal. Issled. Oper., 2009, Volume 16, Number 1, Pages 80–92 (Mi da563)  

This article is cited in 8 scientific papers (total in 8 papers)

On two-colour perfect colourings of circular graphs

D. B. Khoroshilova

Novosibirsk State University

Abstract: We consider perfect colourings of a certain class of infinite graphs called circular graphs. It is shown that every such perfect colouring yields a perfect colouring of an $n$-dimensional infinite lattice which has the same parameters as the original colouring. A construction that produces two-colour perfect colourings of circular graphs is proposed and the parameters of perfect colourings given by the construction are enumerated. Bibl. 12.

Keywords: perfect colouring, circular graph, equitable partition.

Full text: PDF file (269 kB)
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Bibliographic databases:

UDC: 519.87
Received: 16.09.2008
Revised: 17.11.2008

Citation: D. B. Khoroshilova, “On two-colour perfect colourings of circular graphs”, Diskretn. Anal. Issled. Oper., 16:1 (2009), 80–92

Citation in format AMSBIB
\Bibitem{Kho09}
\by D.~B.~Khoroshilova
\paper On two-colour perfect colourings of circular graphs
\jour Diskretn. Anal. Issled. Oper.
\yr 2009
\vol 16
\issue 1
\pages 80--92
\mathnet{http://mi.mathnet.ru/da563}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2543164}
\zmath{https://zbmath.org/?q=an:1249.05119}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Puzynina, “On periodicity of perfect colorings of the infinite hexagonal and triangular grids”, Siberian Math. J., 52:1 (2011), 91–104  mathnet  crossref  mathscinet  isi
    2. S. V. Avgustinovich, M. A. Lisitsyna, “Perfect 2-colorings of transitive cubic graphs”, J. Appl. Industr. Math., 5:4 (2011), 519–528  mathnet  crossref  mathscinet  zmath
    3. S. V. Avgustinovich, A. Yu. Vasil'eva, I. V. Sergeeva, “Distance regular colorings of the infinite rectangular grid”, J. Appl. Industr. Math., 6:3 (2012), 280–285  mathnet  crossref  mathscinet  zmath
    4. D. B. Khoroshilova, “O parametrakh sovershennykh 2-raskrasok tsirkulyantnykh grafov”, Diskretn. analiz i issled. oper., 18:6 (2011), 82–89  mathnet  mathscinet  zmath
    5. M. A. Lisitsyna, “Perfect $3$-colorings of prisms and Möbius ladders”, J. Appl. Industr. Math., 7:2 (2013), 215–220  mathnet  crossref  mathscinet
    6. O. G. Parshina, “Perfect $2$-colorings of infinite circulant graphs with a continuous set of distances”, J. Appl. Industr. Math., 8:3 (2014), 357–361  mathnet  crossref  mathscinet
    7. M. A. Lisitsyna, S. V. Avgustinovich, “Sovershennye raskraski prizmy”, Sib. elektron. matem. izv., 13 (2016), 1116–1128  mathnet  crossref
    8. M. A. Lisitsyna, O. G. Parshina, “Perfect colorings of the infinite circulant graph with distances 1 and 2”, J. Appl. Industr. Math., 11:3 (2017), 381–388  mathnet  crossref  crossref  elib
  • Дискретный анализ и исследование операций
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