Infinite Family of Ramsey (K1,2,C4)-minimal Graphs

F. F. Hadiputra; D. R. Silaban

doi:10.1088/1742-6596/1722/1/012049

Infinite Family of Ramsey (K_1,2,C₄)-minimal Graphs

F. F. Hadiputra
, D. R. Silaban

Department of Mathematics

Research output: Contribution to journal › Conference article › peer-review

2 Citations (Scopus)

Abstract

Suppose F, G, and H be simple graphs. We let F → (G, H) denote red-blue coloring of edges of F containing either red G or blue H. The graph F is considered Ramsey (G, H)-minimal if F → (G, H) and F − e 6→ (G, H) for arbitrary edge e of E(F). The set of (G, H)-minimal graphs is denoted by R(G, H). In this paper, we study an infinite family of graphs belongs to R(K1,2, C4).

Original language	English
Article number	012049
Journal	Journal of Physics: Conference Series
Volume	1722
Issue number	1
DOIs	https://doi.org/10.1088/1742-6596/1722/1/012049
Publication status	Published - 7 Jan 2021
Event	10th International Conference and Workshop on High Dimensional Data Analysis, ICW-HDDA 2020 - Sanur-Bali, Indonesia Duration: 12 Oct 2020 → 15 Oct 2020

Keywords

Cycle graph C
Edge coloring
Path graph K
Ramsey minimal graph

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10.1088/1742-6596/1722/1/012049

Cite this

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title = "Infinite Family of Ramsey (K1,2,C4)-minimal Graphs",

abstract = "Suppose F, G, and H be simple graphs. We let F → (G, H) denote red-blue coloring of edges of F containing either red G or blue H. The graph F is considered Ramsey (G, H)-minimal if F → (G, H) and F − e 6→ (G, H) for arbitrary edge e of E(F). The set of (G, H)-minimal graphs is denoted by R(G, H). In this paper, we study an infinite family of graphs belongs to R(K1,2, C4).",

keywords = "Cycle graph C, Edge coloring, Path graph K, Ramsey minimal graph",

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AU - Hadiputra, F. F.

AU - Silaban, D. R.

N1 - Funding Information: Part of this research is funded by PUTI-UI 2020 Research Grant No. 942/UN2.RST/HKP.05.00/2020. Publisher Copyright: © 2021 Institute of Physics Publishing. All rights reserved. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/1/7

Y1 - 2021/1/7

N2 - Suppose F, G, and H be simple graphs. We let F → (G, H) denote red-blue coloring of edges of F containing either red G or blue H. The graph F is considered Ramsey (G, H)-minimal if F → (G, H) and F − e 6→ (G, H) for arbitrary edge e of E(F). The set of (G, H)-minimal graphs is denoted by R(G, H). In this paper, we study an infinite family of graphs belongs to R(K1,2, C4).

AB - Suppose F, G, and H be simple graphs. We let F → (G, H) denote red-blue coloring of edges of F containing either red G or blue H. The graph F is considered Ramsey (G, H)-minimal if F → (G, H) and F − e 6→ (G, H) for arbitrary edge e of E(F). The set of (G, H)-minimal graphs is denoted by R(G, H). In this paper, we study an infinite family of graphs belongs to R(K1,2, C4).

KW - Cycle graph C

KW - Edge coloring

KW - Path graph K

KW - Ramsey minimal graph

UR - https://www.scopus.com/pages/publications/85100756144

U2 - 10.1088/1742-6596/1722/1/012049

DO - 10.1088/1742-6596/1722/1/012049

M3 - Conference article

AN - SCOPUS:85100756144

SN - 1742-6588

VL - 1722

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012049

T2 - 10th International Conference and Workshop on High Dimensional Data Analysis, ICW-HDDA 2020

Y2 - 12 October 2020 through 15 October 2020

ER -

Infinite Family of Ramsey (K_1,2,C₄)-minimal Graphs

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Keywords

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