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Sib. Èlektron. Mat. Izv., 2004, Volume 1, Pages 117–128 (Mi semr11)  

This article is cited in 9 scientific papers (total in 9 papers)

Research papers

Continuation of a $3$-coloring from a $7$-face onto a plane graph without $3$-cycles

V. A. Aksenova, O. V. Borodinb, A. N. Glebovb

a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We characterize the $3$-colourings of a $7$-face in a plane graph without $3$-cycles that can be extended to a $3$-colouring of the whole graph.

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Bibliographic databases:
UDC: 519.172.2
MSC: 05C15
Received November 18, 2004, published December 14, 2004

Citation: V. A. Aksenov, O. V. Borodin, A. N. Glebov, “Continuation of a $3$-coloring from a $7$-face onto a plane graph without $3$-cycles”, Sib. Èlektron. Mat. Izv., 1 (2004), 117–128

Citation in format AMSBIB
\Bibitem{AksBorGle04}
\by V.~A.~Aksenov, O.~V.~Borodin, A.~N.~Glebov
\paper Continuation of a $3$-coloring from a $7$-face onto a plane graph without $3$-cycles
\jour Sib. \`Elektron. Mat. Izv.
\yr 2004
\vol 1
\pages 117--128
\mathnet{http://mi.mathnet.ru/semr11}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2132453}
\zmath{https://zbmath.org/?q=an:1077.05039}


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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. Borodin O.V., Glebov A.N., Montassier M., Raspaud A., “Planar graphs without 5-and 7-cycles and without adjacent triangles are 3-colorable”, J. Combin. Theory Ser. B, 99:4 (2009), 668–673  crossref  mathscinet  zmath  isi  elib
    2. Borodin O.V., Glebov A.N., Raspaud A., “Planar graphs without triangles adjacent to cycles of length from 4 to 7 are 3-colorable”, Discrete Math., 310:20 (2010), 2584–2594  crossref  zmath  isi  elib
    3. Borodin O.V., Glebov A.N., “Planar Graphs with Neither 5-Cycles Nor Close 3-Cycles Are 3-Colorable”, J Graph Theory, 66:1 (2011), 1–31  crossref  mathscinet  zmath  isi  elib
    4. Borodin O.V., Glebov A.N., Jensen T.R., “A Step Towards the Strong Version of Havel's Three Color Conjecture”, J. Comb. Theory Ser. B, 102:6 (2012), 1295–1320  crossref  mathscinet  mathscinet  zmath  isi  elib
    5. Borodin O.V., Dvorak Z., Kostochka A.V., Lidicky B., Yancey M., “Planar 4-Critical Graphs With Four Triangles”, Eur. J. Comb., 41 (2014), 138–151  crossref  mathscinet  zmath  isi  elib
    6. Dvorak Z., Lidicky B., “3-Coloring Triangle-Free Planar Graphs With a Precolored 8-Cycle”, J. Graph Theory, 80:2 (2015), 98–111  crossref  mathscinet  zmath  isi  elib
    7. Choi I., Ekstein J., Holub P., Lidicky B., “3-Coloring Triangle-Free Planar Graphs With a Precolored 9-Cycle”, Combinatorial Algorithms, Iwoca 2014, Lecture Notes in Computer Science, 8986, eds. Kratochvil J., Miller M., Froncek D., Springer-Verlag Berlin, 2015, 98–109  crossref  mathscinet  zmath  isi
    8. Choi I., Ekstein J., Holu P., Lidicky B., “3-Coloring Triangle-Free Planar Graphs With a Precolored 9-Cycle”, Eur. J. Comb., 68 (2018), 38–65  crossref  mathscinet  zmath  isi  scopus
    9. Dvorak Z., Lidicky B., “Fine Structure of 4-Critical Triangle-Free Graphs i. Planar Graphs With Two Triangles and 3-Colorability of Chains”, SIAM Discret. Math., 32:3 (2018), 1775–1805  crossref  mathscinet  zmath  isi  scopus
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