Aleksandar Bikov

activity

20152019

F_{e} (3, 3; 4)

is greater than 19

7 citations · 19 across the 9 of their papers we have counts for

collaborators

9 papers

math.CO2019

On the independence number of $(3, 3)$ -Ramsey graphs and the Folkman number $F_{e} (3, 3; 4)$

Aleksandar Bikov, Nedyalko Nenov

The graph $G$ is called a $(3, 3)$ -Ramsey graph if in every coloring of the edges of $G$ in two colors there is a monochromatic triangle. The minimum number of vertices of the $(3,…

math.CO2018★ 2 cited

Computation and Bounding of Folkman Numbers

Aleksandar Bikov

PhD Thesis under the supervision of Professor Nedyalko Nenov.

math.CO2017

Lower bounding the Folkman numbers $F_{v} (a_{1}, ..., a_{s}; m - 1)$

Aleksandar Bikov, Nedyalko Nenov

For a graph $G$ the expression $G \to v (a_{1}, ..., a_{s})$ means that for every $s$ -coloring of the vertices of $G$ there exists $i \in {1, ..., s}$ such that th…

math.CO2016

New bounds on the vertex Folkman number $F_{v} (2, 2, 2, 3; 4)$

Aleksandar Bikov

For a graph $G$ the expression $G \to v (a_{1}, ..., a_{s})$ means that for every coloring of the vertices of $G$ in $s$ colors there exists $i \in {1, ..., s}$ su…

math.CO2016★ 7 cited

The edge Folkman number $F_{e} (3, 3; 4)$ is greater than 19

Aleksandar Bikov, Nedyalko Nenov

The set of the graphs which do not contain the complete graph on $q$ vertices $K_{q}$ and have the property that in every coloring of their edges in two colors there exist a monochro…

math.CO2016★ 3 cited

Small minimal $(3, 3)$ -Ramsey graphs

Aleksandar Bikov

We say that $G$ is a $(3, 3)$ -Ramsey graph if every $2$ -coloring of the edges of $G$ forces a monochromatic triangle. The $(3, 3)$ -Ramsey graph $G$ is minimal if $G$ does not conta…

On the independence number of (3,3)-Ramsey graphs and the Folkman number Fe​(3,3;4)

Computation and Bounding of Folkman Numbers

Lower bounding the Folkman numbers Fv​(a1​,...,as​;m−1)

New bounds on the vertex Folkman number Fv​(2,2,2,3;4)

The edge Folkman number Fe​(3,3;4) is greater than 19

Small minimal (3,3)-Ramsey graphs

On the independence number of $(3, 3)$ -Ramsey graphs and the Folkman number $F_{e} (3, 3; 4)$

Lower bounding the Folkman numbers $F_{v} (a_{1}, ..., a_{s}; m - 1)$

New bounds on the vertex Folkman number $F_{v} (2, 2, 2, 3; 4)$

The edge Folkman number $F_{e} (3, 3; 4)$ is greater than 19

Small minimal $(3, 3)$ -Ramsey graphs