• Publications
  • Influence
Path Ramsey Number for Random Graphs
  • Shoham Letzter
  • Mathematics
    Combinatorics, Probability and Computing
  • 26 May 2014
TLDR
It is shown that if pn → ∞, w.h.p., whenever G = G(n, p) is 2-edge-coloured there is a monochromatic path of length (2/3 + o(1))n, which is optimal in the sense that 2/3 cannot be replaced by a larger constant.
Monochromatic Cycle Partitions of 2-Coloured Graphs with Minimum Degree 3n/4
TLDR
This paper proves the conjecture that for every $2$-edge-colouring of G, the vertex set V(G) may be partitioned into two vertex-disjoint cycles, one of each colour.
Three colour bipartite Ramsey number of cycles and paths
The k-colour bipartite Ramsey number of a bipartite graph H is the least integer n for which every k-edge-coloured complete bipartite graph Kn,n contains a monochromatic copy of H. The study of
Large Monochromatic Triple Stars in Edge Colourings
TLDR
It is proved that for every r-edge-colouring of Kn there is a monochromatic triple star of order at least n/r-1, improving Ruszinko's result 2012.
Dense Induced Bipartite Subgraphs in Triangle-Free Graphs
TLDR
It is proved that any H -free graph with minimum degree at least d contains an induced bipartite subgraph of minimum degreeAt least c H log d /log log d , thus nearly confirming one and proving another conjecture of Esperet, Kang and Thomassé.
Directed Ramsey number for trees
Hypergraphs with no tight cycles
We show that every r-uniform hypergraph on n vertices which does not contain a tight cycle has at most O(n(logn)) edges. This is an improvement on the previously best-known bound, of ne √ , due to
3‐Color bipartite Ramsey number of cycles and paths
TLDR
This paper determines asymptotically the $3$-colour bipartite Ramsey number of paths and (even) cycles.
Multicolour Bipartite Ramsey Number of Paths
TLDR
This paper determines asymptotically the $4$-colour bipartite Ramsey number of paths and cycles which are close to being tight and provides new upper bounds on the $k$- Colour bipartites Ramsey numbers which are Close to being Tight.
...
1
2
3
4
5
...