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2013 | 11 | 2 | 308-321
Tytuł artykułu

The structure of plane graphs with independent crossings and its applications to coloring problems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
If a graph G has a drawing in the plane in such a way that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. In this paper, the structure of IC-planar graphs with minimum degree at least two or three is studied. By applying their structural results, we prove that the edge chromatic number of G is Δ if Δ ≥ 8, the list edge (resp. list total) chromatic number of G is Δ (resp. Δ + 1) if Δ ≥ 14 and the linear arboricity of G is ℈Δ/2⌊ if Δ ≥ 17, where G is an IC-planar graph and Δ is the maximum degree of G.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
2
Strony
308-321
Opis fizyczny
Daty
wydano
2013-02-01
online
2012-11-21
Twórcy
Bibliografia
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  • [8] Erman R., Havet F., Lidický B., Pangrác O., 5-coloring graphs with 4 crossings, SIAM J. Discrete Math., 2011, 25(1), 401–422 http://dx.doi.org/10.1137/100784059
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  • [14] Ringel G., Ein Sechsfarbenproblem auf der Kugel, Abh. Math. Sem. Univ. Hamburg, 1965, 29, 107–117 http://dx.doi.org/10.1007/BF02996313
  • [15] Sanders D.P., Zhao Y., On total 9-coloring planar graphs of maximum degree seven, J. Graph Theory, 1999, 31(1), 67–73 http://dx.doi.org/10.1002/(SICI)1097-0118(199905)31:1<67::AID-JGT6>3.0.CO;2-C
  • [16] Sanders D.P., Zhao Y., Planar graphs of maximum degree seven are class I, J. Combin. Theory Ser. B, 2001, 83(2), 201–212 http://dx.doi.org/10.1006/jctb.2001.2047
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  • [18] Wu J.-L., On the linear arboricity of planar graphs, J. Graph Theory, 1999, 31(2), 129–134 http://dx.doi.org/10.1002/(SICI)1097-0118(199906)31:2<129::AID-JGT5>3.0.CO;2-A
  • [19] Wu J., Wang P., List-edge and list-total colorings of graphs embedded on hyperbolic surfaces, Discrete Math., 2008, 308(4), 6210–6215 http://dx.doi.org/10.1016/j.disc.2007.11.044
  • [20] Wu J.-L., Wu Y.-W., The linear arboricity of planar graphs of maximum degree seven is four, J. Graph Theory, 2008, 58(3), 210–220 http://dx.doi.org/10.1002/jgt.20305
  • [21] Zhang X., Hou J., Liu G., On total colorings of 1-planar graphs, preprint available at http://xinzhang.hpage.com/get_file.php?id=1513981&vnr=342077
  • [22] Zhang X., Wu J.-L., On edge colorings of 1-planar graphs, Inform. Process. Lett., 2011, 111(3), 124–128 http://dx.doi.org/10.1016/j.ipl.2010.11.001
  • [23] Zhang X., Wu J., Liu G., List edge and list total coloring of 1-planar graphs, Front. Math. China (in press), DOI: 10.1007/s11464-012-0184-7
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-012-0094-7
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