• Corpus ID: 5716507

ON THE MAGNITUDE OF GENERALIZED RAMSEY NUMBERS FOR GRAPHS

@inproceedings{Burr1973ONTM,
  title={ON THE MAGNITUDE OF GENERALIZED RAMSEY NUMBERS FOR GRAPHS},
  author={Stefan A. Burr},
  year={1973}
}
If G and H are graphs (which will mean finite, with no loops or parallel lines), define the Ramsey number r(G, H) to be the least number p such that if the lines of the complete graph Kp are colored red and blue (say), either the red subgraph contains a copy of G or the blue subgraph contains H. The diagonal Ranisei , numbers are given by r(G) _ = r(G, G) . These definitions follow those of C h v á t a I and H a r a r y[ 1 ] . Otlier terminology will follow H a r a r y [ 2] . These generalized… 

Figures from this paper

Extremal Ramsey theory for graphs

If G and H are graphs, define the Ramsey number to be the least number p such that if the lines of the complete graph Kp are colored red and blue (say),either the red subgraph contains a copy of G or

Topics in flnite graph Ramsey theory

For a positive integer r and graphs F , G, and H, the graph Ramsey arrow notation F −→ (G)r means that for every r-colouring of the subgraphs of F isomorphic to H, there exists a subgraph G′ of F

On graphs with linear Ramsey numbers

TLDR
In this paper, the use of the regularity lemma is avoided altogether, and it is shown that one can in fact take, for some ®xed c, c… † < 2 (log )2 in the general case, and even even 1.

On graphs with small Ramsey numbers *

TLDR
It is shown that for every positive integer d and each,0< <1, there exists kˆ k (d, ) such that forevery bipartite graph Gˆ (W,U;E ) with the maximum degree of vertices in W at most d and jU j j jW j, R (G ) k jWJ.

Ordered Ramsey numbers

THE SIZE-RAMSEY NUMBER

The size-Ramsey number of a graph G is the smallest number of edges in a graph Γ with the Ramsey property for G, that is, with the property that any colouring of the edges of Γ with two colours (say)

On Ramsey Numbers of Sparse Graphs

TLDR
It is shown that, for every , sufficiently large n, and any graph H of order , either H or its complement contains a (d,n)-common graph, that is, a graph in which every set of d vertices has at least n common neighbours.
...

References

SHOWING 1-3 OF 3 REFERENCES

Generalized Ramsey theory for graphs

The classical Ramsey numbers [7] involve the occurrence of monochromatic complete subgraphs in line-colored complete graphs. By removing the completeness requirements and admitting arbitrary

Generalized ramsey theory for graphs - a survey

Almost nonexistent a few years ago, the field of generalized Ramsey theory for graphs is now being pursued very actively and with remarkable success. This survey paper will emphasize the following

B u r r-P . E r d ő s, Extremal Ramsey Theory for Graphs

  • B u r r-P . E r d ő s, Extremal Ramsey Theory for Graphs