The Classical Ramsey Number R(3,4)>8 Using the Weighted Graph - Khairul Azmi; Elva; Widia (Rangkiang Mathematics Journal, 2022)
At present, research on Ramsey Numbers has expanded to a wider scope, not only between 2 complete graphs that are complementary to each other but also a combination of complete graphs, circle graphs, star graphs, wheel graphs, and others. While the classic Ramsey number still leaves problems that need to be solved. Ramsey number R(3,4) > 8. This means that m=8 is the largest integer such that K_(8) which contains components of a red graph G and a complete blue graph G which is still possible not to get K_3 in graph G and not get a blue K_4 in graph G .The graph K_(8) has a total of 28 edges. There are as many as the combination (28,3) red edge pairs that need to be avoided so as not to get any red K_3 edge pairs. And there are as many as the combination (28,4) edge pairs blue. That needs to be avoided in order not to get a pair of blue K_4 edges. Determining the coloring of the of the graph directly is certainly very difficult, especially if the Ramsey number is getting bigger. It's like looking for a needle in a haystack. Need to use a special method in order to solve this problem. The weighting graph method, where each edge is given weight with a certain value, is able to solve this problem. The weighting graph method is able to display the graph K_8 in the form of a G matrix with the order of 8×8.