On Ramsey Minimal Graphs for a 3-Matching Versus a Path on Five Vertices
Kristiana Wijaya1, *, Edy Tri Baskoro2, Asep Iqbal Taufik3, Denny Riama Silaban3
1Graph, Combinatorics, and Algebra Research Group, Department of Mathematics, FMIPA, Universitas Jember
2Combinatorial Mathematics Research Group, FMIPA, Institut Teknologi Bandung
3Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424
*Corresponding author. Email: firstname.lastname@example.org
Available Online 8 February 2022.
- 10.2991/acsr.k.220202.001How to use a DOI?
- Ramsey minimal graph; 3-matching; Path
Let G, H, and F be simple graphs. The notation F ⟶ (G, H) means that any red-blue coloring of all edges of F contains a red copy of G or a blue copy of H. The graph F satisfying this property is called a Ramsey (G, H)-graph. A Ramsey (G, H)-graph is called minimal if for each edge e ∈ E(F), there exists a red-blue coloring of F − e such that F − e contains neither a red copy of G nor a blue copy of H. In this paper, we construct some Ramsey (3K2, P5)-minimal graphs by subdivision (5 times) of one cycle edge of a Ramsey (2K2, P5)-minimal graph. Next, we also prove that for any integer m ≥ 3, the set R(mK2, P5) contains no connected graphs with circumference 3.
- © 2022 The Authors. Published by Atlantis Press International B.V.
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Cite this article
TY - CONF AU - Kristiana Wijaya AU - Edy Tri Baskoro AU - Asep Iqbal Taufik AU - Denny Riama Silaban PY - 2022 DA - 2022/02/08 TI - On Ramsey Minimal Graphs for a 3-Matching Versus a Path on Five Vertices BT - Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021) PB - Atlantis Press SP - 1 EP - 4 SN - 2352-538X UR - https://doi.org/10.2991/acsr.k.220202.001 DO - 10.2991/acsr.k.220202.001 ID - Wijaya2022 ER -