Monochromatic Cycles in 2-Coloured Graphs

@article{Benevides2012MonochromaticCI,
  title={Monochromatic Cycles in 2-Coloured Graphs},
  author={Fabricio Siqueira Benevides and Tomasz Luczak and Alex D. Scott and Jozef Skokan and M. White},
  journal={Combinatorics, Probability & Computing},
  year={2012},
  volume={21},
  pages={57-87}
}
Li, Nikiforov and Schelp [12] conjectured that any 2-edge coloured graph G with order n and minimum degree δ(G) > 3n/4 contains a monochromatic cycle of length `, for all ` ∈ [4, dn/2e]. We prove this conjecture for sufficiently large n and also find all 2-edge coloured graphs with δ(G) = 3n/4 that do not contain all such cycles. Finally, we show that, for all δ > 0 and n > n0(δ), if G is a 2-edge coloured graph of order n with δ(G) ≥ 3n/4, then one colour class either contains a monochromatic… CONTINUE READING

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References

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Showing 1-10 of 14 references

Pancyclic graphs I

  • J. Bondy
  • J. Comb. Theory, Ser. B,
  • 1971
Highly Influential
6 Excerpts

Sur le couplage maximum d’un graphe

  • C. Berge
  • C.R. Acad. Sci. Paris,
  • 1958
Highly Influential
4 Excerpts

Some theorems on abstract graphs

  • G. Dirac
  • Proc. London Math. Soc.,
  • 1952
Highly Influential
4 Excerpts

Cycles of even lengths in graphs

  • J. Bondy, M. Simonovits
  • J. Comb. Theory, Ser. B,
  • 1974
Highly Influential
3 Excerpts

Graphs with large minimum degrees arrow even cycles

  • B. Bollobás, F. Benevides, T. Luczak, J. Skokan
  • 2011
1 Excerpt

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