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  • Cited by 17
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Barát, János and Sárközy, Gábor N. 2016. Partitioning 2-Edge-Colored Ore-Type Graphs by Monochromatic Cycles. Journal of Graph Theory, Vol. 81, Issue. 4, p. 317.


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    Grinshpun, Andrey and Sárközy, Gábor N. 2016. Monochromatic bounded degree subgraph partitions. Discrete Mathematics, Vol. 339, Issue. 1, p. 46.


    Gyárfás, András Sárközy, Gábor N. and Selkow, Stanley 2015. Coverings by Few Monochromatic Pieces: A Transition Between Two Ramsey Problems. Graphs and Combinatorics, Vol. 31, Issue. 1, p. 131.


    Lang, Richard and Stein, Maya 2015. Local colourings and monochromatic partitions in complete bipartite graphs. Electronic Notes in Discrete Mathematics, Vol. 49, p. 757.


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    Balogh, József Barát, János Gerbner, Dániel Gyárfás, András and Sárközy, Gábor N. 2014. Partitioning 2-edge-colored graphs by monochromatic paths and cycles. Combinatorica, Vol. 34, Issue. 5, p. 507.


    Pokrovskiy, Alexey 2014. Partitioning edge-coloured complete graphs into monochromatic cycles and paths. Journal of Combinatorial Theory, Series B, Vol. 106, p. 70.


    Sárközy, Gábor N. 2014. Improved monochromatic loose cycle partitions in hypergraphs. Discrete Mathematics, Vol. 334, p. 52.


    Allen, Peter Brightwell, Graham and Skokan, Jozef 2013. Ramsey-goodness—and otherwise. Combinatorica, Vol. 33, Issue. 2, p. 125.


    Pokrovskiy, Alexey 2013. Partitioning edge-coloured complete graphs into monochromatic cycles. Electronic Notes in Discrete Mathematics, Vol. 43, p. 311.


    Sárközy, Gábor N. Selkow, Stanley M. and Song, Fei 2013. An Improved Bound for Vertex Partitions by Connected Monochromatic K-Regular Graphs. Journal of Graph Theory, Vol. 73, Issue. 2, p. 127.


    Pokrovskiy, Alexey 2011. Partitioning 3-coloured complete graphs into three monochromatic paths. Electronic Notes in Discrete Mathematics, Vol. 38, p. 717.


    Sárközy, Gábor N. 2011. Monochromatic cycle partitions of edge-colored graphs. Journal of Graph Theory, Vol. 66, Issue. 1, p. 57.


    Sárközy, Gábor N. Selkow, Stanley M. and Song, Fei 2011. Vertex partitions of non-complete graphs into connected monochromatic <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>k</mml:mi></mml:math>-regular graphs. Discrete Mathematics, Vol. 311, Issue. 18-19, p. 2079.


    Bessy, Stéphane and Thomassé, Stéphan 2010. Partitioning a graph into a cycle and an anticycle, a proof of Lehel's conjecture. Journal of Combinatorial Theory, Series B, Vol. 100, Issue. 2, p. 176.


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  • Combinatorics, Probability and Computing, Volume 17, Issue 4
  • July 2008, pp. 471-486

Covering Two-Edge-Coloured Complete Graphs with Two Disjoint Monochromatic Cycles

  • PETER ALLEN (a1)
  • DOI: http://dx.doi.org/10.1017/S0963548308009164
  • Published online: 01 July 2008
Abstract

In 1998 Łuczak Rödl and Szemerédi [7] proved, by means of the Regularity Lemma, that there exists n0 such that, for any nn0 and two-edge-colouring of Kn, there exists a pair of vertex-disjoint monochromatic cycles of opposite colours covering the vertices of Kn. In this paper we make use of an alternative method of finding useful structure in a graph, leading to a proof of the same result with a much smaller value of n0. The proof gives a polynomial-time algorithm for finding the two cycles.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]P. Erdős , A. Gyárfás and L. Pyber (1991) Vertex coverings by monochromatic cycles and trees. J. Combin. Theory Ser. B 51 9095.

[3]A. Gyárfás (1983) Vertex coverings by monochromatic paths and cycles. J. Graph Theory 7 131135.

[4]A. Gyárfás , M. Ruszinkó G. N. Sárközy and E. Szemerédi (2006) An improved bound for the monochromatic cycle partition number. J. Combin. Theory Ser. B 96 855873.

[5]J. Komlós , G. N. Sárközy and E. Szemerédi (1997) Blow-up lemma. Combinatorica 17 109123.

[7]T. Łuczak , V. Rödl and E. Szemerédi (1998) Partitioning two-coloured complete graphs into two monochromatic cycles. Combin. Probab. Comput. 7 423436.

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  • ISSN: 0963-5483
  • EISSN: 1469-2163
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