Rangkiang Mathematics Journal
Vol. 1 No. 1 (2022): Rangkiang Mathematics Journal

The Classical Ramsey Number R(3,4)>8 Using the Weighted Graph

Khairul Azmi (Universitas Adzkia)
Elva (Universitas Adzkia)
Widia (Universitas Adzkia)



Article Info

Publish Date
26 Apr 2022

Abstract

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.

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Journal Info

Abbrev

RMJ

Publisher

Subject

Mathematics Other

Description

Rangkiang Mathematics Journal (RMJ) is a prestigious vision journal which focuses on publishing research, and advance literature study in mathematics and mathematics education. The scope of this journal includes: mathematics teacher profesionalisme, Realistic Mathematics Education, ...