Connected Size Ramsey Numbers for The Pair Complete Graph of Order Two versus Union Complete Graph of Order Three

Authors

  • Hasmawati Hasmawati Department of Mathematics, Faculty of Mathematics and Natural Sciences, Hasanuddin University, Indonesia
  • Sri Indrayani Department of Mathematics, Faculty of Mathematics and Natural Sciences, Hasanuddin University, Indonesia

DOI:

https://doi.org/10.20956/j.v21i2.41850

Keywords:

graph; connected; size Ramsey number; complete graph., connected, size Ramsey number, complete graph

Abstract

Let F,G, and H be finite, simple, and undirected graphs. The connected size Ramsey number r ̂_c (G,H) of graph G and H is the least integer k such that there is a connected graph F with k edges and if the edge set of F is arbitrarily colored by red or blue, then there always exists either a red copy of G or a blue copy of H. This paper shows that the connected size Ramsey number r ̂_c (2K_2,〖nK〗_3 )=4n+3, for n≥4.

References

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Published

2025-01-12

How to Cite

Hasmawati, H., & Indrayani, S. (2025). Connected Size Ramsey Numbers for The Pair Complete Graph of Order Two versus Union Complete Graph of Order Three . Jurnal Matematika, Statistika Dan Komputasi, 21(2), 601–607. https://doi.org/10.20956/j.v21i2.41850

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Section

Research Articles

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