University of Birmingham > Talks@bham > Combinatorics and Probability Seminar > Edges not in any monochromatic copy of a fixed graph

## Edges not in any monochromatic copy of a fixed graphAdd to your list(s) Download to your calendar using vCal - Maryam Sharifzadeh (Warwick)
- Thursday 16 March 2017, 15:00-16:00
- LTC Watson.
If you have a question about this talk, please contact Dr Andrew Treglown. For a family of fixed graphs H_1,...,H_k, denote by f(n;H_1,..., H_k) the maximum number of edges not contained in any monochromatic copy of H_i in colour i, in a k-edge-colouring of K_n. It is easy to see that $f(n;H,H)\ge\ex(n,H)$. In this talk, we introduce a new variant of Ramsey number, which determines f(n;H_1,..., H_k) asymptotically for non-bipartite graphs H_i. For the 3-colour case, an exact result is obtained for a subfamily of colour-critical graphs, including cliques. The special case f(n;K_3,K_3,K_3) answers a question of Ma affirmatively. For bipartite graphs, Keevash and Sudakov showed $f(n;C_4,C_4)=\ex(n,C_4)$; recently Ma extended their result to an infinite family of bipartite graphs. We provide a larger family of bipartite graphs for which $f(n;H,H)=\ex(n,H)$. For general bipartite graphs, we prove an upper bound with an additive error term, i.e. $f(n;H,H)\le \ex(n,H)+O(1)$. This talk is part of the Combinatorics and Probability Seminar series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
## Other listsCold atoms Condensed Matter Group Meetings Particle Physics Seminars## Other talksPerfect matchings in random sparsifications of Dirac hypergraphs Geometry of alternating projections in metric spaces with bounded curvature Quantum simulations using ultra cold ytterbium The development of an optically pumped magnetometer based MEG system Hodge Theory: Connecting Algebra and Analysis Ultrafast, all-optical, and highly efficient imaging of molecular chirality |