Ramsey Graphs for a Star on Three Vertices Versus a Cycle
Authors
Maya Nabila*, Edy Tri Baskoro, Hilda Assiyatun
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
*Corresponding author. Email: mayanabila@students.itb.ac.id
Corresponding Author
Maya Nabila
Available Online 8 February 2022.
- DOI
- 10.2991/acsr.k.220202.002How to use a DOI?
- Keywords
- Ramsey minimal graph; Star; Cycle
- Abstract
Let G, A, and B be simple graphs. The notation G → (A, B) means that for any red-blue coloring of the edges of G, there is a red copy of A or a blue copy of B in G. A graph G is called a Ramsey graph for (A, B) if G → (A, B). Additionally, if the graph G satisfies that G − e ↛ (A, B), for any e ∈ E(G), then G is called a Ramsey (A, B)-minimal graph. The set of all Ramsey (A, B)-minimal graphs is denoted by ℛ(A, B). In this paper, we study the Ramsey (Cn, K1,2)-minimal graphs. Specifically, we give some Ramsey (Cn, K1,2)-minimal graphs for any n ∈ [7,10]. We also construct Ramsey (Cn, K1,2)-graphs from the well-known Harary graph, for any integer n ≥ 6.
- Copyright
- © 2022 The Authors. Published by Atlantis Press International B.V.
- Open Access
- This is an open access article under the CC BY-NC license.
Cite this article
TY - CONF AU - Maya Nabila AU - Edy Tri Baskoro AU - Hilda Assiyatun PY - 2022 DA - 2022/02/08 TI - Ramsey Graphs for a Star on Three Vertices Versus a Cycle BT - Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021) PB - Atlantis Press SP - 5 EP - 10 SN - 2352-538X UR - https://doi.org/10.2991/acsr.k.220202.002 DO - 10.2991/acsr.k.220202.002 ID - Nabila2022 ER -