Some intersection theorems for ordered sets and graphs
Journal of Combinatorial Theory Series A
The number of edge colorings with no monochromatic triangle
Journal of Graph Theory
On colourings of hypergraphs without monochromatic fano planes
Combinatorics, Probability and Computing
Hypergraphs with many Kneser colorings
European Journal of Combinatorics
Edge colourings of graphs avoiding monochromatic matchings of a given size
Combinatorics, Probability and Computing
| Hi-index | 0.00 |
Fix a graph F and a positive integer r. With a graph G, we associate the quantity c"r","F(G), the number of r-colorings of the edge set of G with no monochromatic copy of F as a subgraph. Consider the function c"r","F:N@?N given by c"r","F(n)=max{c"r","F(G):|V(G)|=n}, the maximum of c"r","F(G) over all graphs G on n vertices. In this paper we study the asymptotic behavior of c"r","F(n) and describe the extremal graphs for some forbidden graphs F with linear Turan number, such as small paths, stars and trees.