On Ramsey (mK2, P4)-Minimal Graphs

dc.contributor.author	TAUFIK, Asep Iqbal
dc.contributor.author	SILABAN, Denny Riama
dc.contributor.author	WIJAYA, Kristiana
dc.date.accessioned	2023-02-23T02:22:24Z
dc.date.available	2023-02-23T02:22:24Z
dc.date.issued	2021
dc.identifier.uri	https://repository.unej.ac.id/xmlui/handle/123456789/112331
dc.description.abstract	Let 𝐹, 𝐺, and 𝐻 be simple graphs. 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. Graph 𝐹 is a Ramsey (𝐺, 𝐻)-minimal if 𝐹 → (𝐺, 𝐻) but for each 𝑒 ∈ 𝐸(𝐹), (𝐹 − 𝑒) ↛ (𝐺, 𝐻). The set ℛ(𝐺, 𝐻) consists of all Ramsey (𝐺, 𝐻)-minimal graphs. Let 𝑚𝐾2 be matching with m edges and 𝑃𝑛 be a path on n vertices. In this paper, we construct all disconnected Ramsey minimal graphs, and found some new connected graphs in ℛ(3𝐾2 , 𝑃4 ). Furthermore, we also construct new Ramsey minimal graphs in ℛ((𝑚 + 1)𝐾2 , 𝑃4) from Ramsey minimal graphs in ℛ(𝑚𝐾2 , 𝑃4) for 𝑚 ≥ 4, by subdivision operation.	en_US
dc.language.iso	en	en_US
dc.publisher	Atlantis Press	en_US
dc.subject	Matching	en_US
dc.subject	Path	en_US
dc.subject	Ramsey minimal graphs	en_US
dc.subject	Subdivision	en_US
dc.title	On Ramsey (mK2, P4)-Minimal Graphs	en_US
dc.type	Article	en_US