Ramsey Graphs for a Star on Three Vertices Versus a Cycle

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 (C_n, K_1,2)-minimal graphs. Specifically, we give some Ramsey (C_n, K_1,2)-minimal graphs for any n ∈ [7,10]. We also construct Ramsey (C_n, K_1,2)-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.

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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  -