Please use this identifier to cite or link to this item: https://repository.unej.ac.id/xmlui/handle/123456789/112311
Title: Subdivision of graphs in R(mK2,P4)
Authors: WIJAYA, Kristiana
BASKORO, Edy Tri
ASSIYATUN, Hilda
SUPRIJANTO, Djoko
Keywords: Mathematics Ramsey minimal graphs Red-blue coloring Matching Path
Issue Date: 12-Jun-2020
Publisher: Heliyon
Abstract: For any graphs 𝐹 ,𝐺, and 𝐻, the notation 𝐹 → (𝐺,𝐻) means that any red-blue coloring of all edges of 𝐹 will contain either a red copy of 𝐺 or a blue copy of 𝐻. The set (𝐺,𝐻) consists of all Ramsey (𝐺,𝐻)-minimal graphs, namely all graphs 𝐹 satisfying 𝐹 → (𝐺,𝐻) but for each 𝑒 ∈ 𝐸(𝐹), (𝐹 − 𝑒) ↛ (𝐺,𝐻). In this paper, we propose a simple construction for creating new Ramsey minimal graphs from the previous known Ramsey minimal graphs (by subdivision operation). In particular, suppose 𝐹 ∈ (𝑚𝐾2,𝑃4) and let 𝑒 ∈ 𝐸(𝐹) be an edge contained in a cycle of 𝐹, we construct a new Ramsey minimal graph in ((𝑚 + 1)𝐾2,𝑃4) from graph 𝐹 by subdividing the edge 𝑒 four time
URI: https://repository.unej.ac.id/xmlui/handle/123456789/112311
Appears in Collections:LSP-Jurnal Ilmiah Dosen

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