Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)

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On Ramsey Minimal Graphs for a 3-Matching Versus a Path on Five Vertices

Authors
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: kristiana.fmipa@unej.ac.id
Corresponding Author
Kristiana Wijaya
Available Online 8 February 2022.
DOI
10.2991/acsr.k.220202.001How to use a DOI?
Keywords
Ramsey minimal graph; 3-matching; Path
Abstract

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.

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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Volume Title
Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)
Series
Advances in Computer Science Research
Publication Date
8 February 2022
ISBN
10.2991/acsr.k.220202.001
ISSN
2352-538X
DOI
10.2991/acsr.k.220202.001How to use a DOI?
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

risenwbib
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  -