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Monochromatic Cycles in 2-Coloured Graphs
| Content Provider | Scilit |
|---|---|
| Author | Benevides, F. S. Łuczak, T. Scott, A. Skokan, J. White, M. |
| Copyright Year | 2012 |
| Description | Li, Nikiforov and Schelp [13] conjectured that any 2-edge coloured graph G with order n and minimum degree δ(G) > 3n/4 contains a monochromatic cycle of length ℓ, for all ℓ ∈ [4, ⌈n/2⌉]. 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 $n>n_{0}$(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 cycle of length at least (2/3+δ/2)n, or contains monochromatic cycles of all lengths ℓ ∈ [3, (2/3−δ)n]. |
| Related Links | http://eprints.lse.ac.uk/43289/1/Skokan_Monochromatic_cycles_2-coloured_2012.pdf https://core.ac.uk/download/pdf/2705149.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/7B4BEFC8371E99F798A686256FAB5726/S0963548312000090a.pdf/div-class-title-monochromatic-cycles-in-2-coloured-graphs-div.pdf |
| Ending Page | 87 |
| Page Count | 31 |
| Starting Page | 57 |
| ISSN | 09635483 |
| e-ISSN | 14692163 |
| DOI | 10.1017/s0963548312000090 |
| Journal | Combinatorics, Probability and Computing |
| Issue Number | 1-2 |
| Volume Number | 21 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2012-03-01 |
| Access Restriction | Open |
| Subject Keyword | Combinatorics, Probability and Computing Order N coloured Graph edge Coloured Graph Monochromatic Cycle Large N Minimum Degree Colour Class |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics |
