On the Nonexistence of Some Generalized Folkman Numbers

@article{Xu2018OnTN,
  title={On the Nonexistence of Some Generalized Folkman Numbers},
  author={Xiaodong Xu and Meilian Liang and S. Radziszowski},
  journal={Graphs and Combinatorics},
  year={2018},
  volume={34},
  pages={1101-1110}
}
For an undirected simple graph G, we write $$G \rightarrow (H_1, H_2)^v$$G→(H1,H2)v if and only if for everyred-blue coloring of its vertices there exists a red $$H_1$$H1 or a blue $$H_2$$H2. Thegeneralized vertex Folkman number $$F_v(H_1, H_2; H)$$Fv(H1,H2;H) is defined as the smallest integer n for which there exists an H-free graph G of order n such that $$G \rightarrow (H_1, H_2)^v$$G→(H1,H2)v. The generalized edge Folkman numbers $$F_e(H_1, H_2; H)$$Fe(H1,H2;H) are defined similarly, when… Expand
2 Citations
A Note on Upper Bounds for Some Generalized Folkman Numbers
  • 2
  • PDF
Computation and Bounding of Folkman Numbers
  • 1
  • PDF

References

SHOWING 1-10 OF 25 REFERENCES
On the Vertex Folkman Numbers $F_v(2,...,2;q)$
  • 8
  • PDF
Graphs with Monochromatic Complete Subgraphs in Every Edge Coloring
  • 187
A multiplicative inequality for vertex Folkman numbers
  • N. Kolev
  • Mathematics, Computer Science
  • Discret. Math.
  • 2008
  • 7
  • PDF
On Ks-free subgraphs in Ks+k-free graphs and vertex Folkman numbers
  • 30
  • PDF
The Ramsey property for graphs with forbidden complete subgraphs
  • 139
  • Highly Influential
Explicit Construction of Small Folkman Graphs
  • L. Lu
  • Mathematics, Computer Science
  • SIAM J. Discret. Math.
  • 2008
  • 21
  • PDF
On Some Open Questions for Ramsey and Folkman Numbers
  • 11
Upper and lower bounds for Fv(4,4;5)
  • 11
Use of MAX-CUT for Ramsey Arrowing of Triangles
  • 12
  • PDF
...
1
2
3
...