Add to ORKGThe Ramsey number r(C_k, C_k, C_k), denoted as r_3(C_k), is the smallest positive integer n such that any edge coloring with three colors of the complete graph on n vertices must contain at least one monochromatic cycle C_k. In this project, most literature on the Ramsey numbers r_3(C_k) are overviewed. Algorithms to check if a graph G contains any specific path or cycle and to construct extremal graphs for cycle C_k are developed. All good 3-colorings of complete graph K_10 are constructed to verify the value of Ramsey number r_3(C_4). Ramsey number value of r_3(C_3) is verified by direct point by point extension algorithm. The lower bounds for the Ramsey numbers r_3(C_5), r_3(C_6), and r_3(C_7) are provided as well. Additionally, the poss...
Using computer algorithms we establish that the Ramsey number R(3, K-10 - e) is equal to 37, which s...
AbstractBy applying a look-ahead algorithm, we show that there are, up to isomorphism, exactly two c...
AbstractFor given graphs G1,G2,G3, the three-color Ramsey number R(G1,G2,G3) is defined to be the le...
AbstractFor given graphs G1,G2,G3, the three-color Ramsey number R(G1,G2,G3) is defined to be the le...
The classical Ramsey Number R(3, 3, 3, 3), which is the smallest positive integer n such that any ed...
The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the com...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
Establishing the values of Ramsey numbers is, in general, a difficult task from the computational po...
The Ramsey number r(K 3,Q n ) is the smallest integer N such that every red-blue colouring of the ed...
The Ramsey number r(Cℓ, Kn) is the smallest natural number N such that every red/blue edge-colouring...
The Ramsey number r(Cℓ, Kn) is the smallest natural number N such that every red/blue edge-colouring...
For graphs G1, G2, G3, the three-color Ramsey number R(G1, G2, G3) is the smallest integer n such th...
The Ramsey number r(K 3,Q n ) is the smallest integer N such that every red-blue colouring of the ed...
Using computational techniques we derive six new upper bounds on the classical two-color Ramsey numb...
Using computer algorithms we establish that the Ramsey number R(3, K-10 - e) is equal to 37, which s...
AbstractBy applying a look-ahead algorithm, we show that there are, up to isomorphism, exactly two c...
AbstractFor given graphs G1,G2,G3, the three-color Ramsey number R(G1,G2,G3) is defined to be the le...
AbstractFor given graphs G1,G2,G3, the three-color Ramsey number R(G1,G2,G3) is defined to be the le...
The classical Ramsey Number R(3, 3, 3, 3), which is the smallest positive integer n such that any ed...
The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the com...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring...
Establishing the values of Ramsey numbers is, in general, a difficult task from the computational po...
The Ramsey number r(K 3,Q n ) is the smallest integer N such that every red-blue colouring of the ed...
The Ramsey number r(Cℓ, Kn) is the smallest natural number N such that every red/blue edge-colouring...
The Ramsey number r(Cℓ, Kn) is the smallest natural number N such that every red/blue edge-colouring...
For graphs G1, G2, G3, the three-color Ramsey number R(G1, G2, G3) is the smallest integer n such th...
The Ramsey number r(K 3,Q n ) is the smallest integer N such that every red-blue colouring of the ed...
Using computational techniques we derive six new upper bounds on the classical two-color Ramsey numb...
Using computer algorithms we establish that the Ramsey number R(3, K-10 - e) is equal to 37, which s...
AbstractBy applying a look-ahead algorithm, we show that there are, up to isomorphism, exactly two c...
AbstractFor given graphs G1,G2,G3, the three-color Ramsey number R(G1,G2,G3) is defined to be the le...