Geodesic
A Note on Upper Bounds for Some Generalized Folkman Numbers
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 4, pp. 939-950

Voir la notice de l'article provenant de la source Library of Science

We present some new constructive upper bounds based on product graphs for generalized vertex Folkman numbers. They lead to new upper bounds for some special cases of generalized edge Folkman numbers, including the cases Fe(K3, K4 − e; K5) ≤ 27 and Fe(K4 − e, K4 − e; K5) ≤ 51. The latter bound follows from a construction of a K5-free graph on 51 vertices, for which every edge coloring with two colors contains a monochromatic K4 − e.
Keywords: Folkman number, Ramsey number 
@article{DMGT_2019_39_4_a13,
     author = {Xu, Xiaodong and Liang, Meilian and Radziszowski, Stanis{\l}aw},
     title = {A {Note} on {Upper} {Bounds} for {Some} {Generalized} {Folkman} {Numbers}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {939--950},
     publisher = {mathdoc},
     volume = {39},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2019_39_4_a13/}
}
TY  - JOUR
AU  - Xu, Xiaodong
AU  - Liang, Meilian
AU  - Radziszowski, Stanisław
TI  - A Note on Upper Bounds for Some Generalized Folkman Numbers
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2019
SP  - 939
EP  - 950
VL  - 39
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2019_39_4_a13/
LA  - en
ID  - DMGT_2019_39_4_a13
ER  - 
%0 Journal Article
%A Xu, Xiaodong
%A Liang, Meilian
%A Radziszowski, Stanisław
%T A Note on Upper Bounds for Some Generalized Folkman Numbers
%J Discussiones Mathematicae. Graph Theory
%D 2019
%P 939-950
%V 39
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2019_39_4_a13/
%G en
%F DMGT_2019_39_4_a13
Xu, Xiaodong; Liang, Meilian; Radziszowski, Stanisław. A Note on Upper Bounds for Some Generalized Folkman Numbers. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 4, pp. 939-950. http://geodesic.mathdoc.fr/item/DMGT_2019_39_4_a13/