Bilangan ramsey untuk graf bintang dan graf siklus

Authors

  • Miftahul Hidayah UIN MALANG

Keywords:

Ramsey Number, Star Graph, Cycle Graph, Graph Theory, Combinatorics

Abstract

Ramsey theory is a branch of combinatorics that studies the existence of specific structures within edge colored complete graphs. This paper examines Ramsey numbers for the pair consisting of a star graph  and cycle graph . The aim of this study is to present the theoretical foundations, basic properties, and main results concerning the exact value of  based on existing literature. The method used is a literature review focusing on the results of Parsons and Lawrence as well as recent developments. The results show that the Ramsey number for this pair depends on the parity of the cycle and the relationship between  and , yielding three main cases covering small odd cycles, small even cycles, and long cycles. In addition, common proof techniques are discussed, including critical graph constructions, degree analysis, and applications of Dirac’s and Turán’s theorems. This study also highlights several generalizations of Ramsey numbers, such as multipartite, wheel graphs, multicolor versions, and long even cycles.

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References

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Published

2026-11-02

How to Cite

Hidayah, M. (2026). Bilangan ramsey untuk graf bintang dan graf siklus. Maliki Interdisciplinary Journal, 4(11), 1611–1617. Retrieved from https://urj.uin-malang.ac.id/index.php/mij/article/view/26238

Issue

Vol. 4 No. 11 (2026): NOVEMBER

Section

Articles

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Copyright (c) 2026 Miftahul Hidayah

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