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[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2015, Springer Basel.Let G and H be any graphs without isolated vertices. The Ramsey set $${\mathcal{R}(G,H)}$$R(G,H) consists of all graphs F without isolated vertices such that $${F \rightarrow (G,H)}$$F→(G,H) and $${F-e \nrightarrow(G,H)}$$F-e↛(G,H) for every $${e \in E(F)}$$e∈E(F). In this paper, we give necessary and sufficient conditions of graphs belonging to the set $${\mathcal{R}(3K_2,K_{1,n})}$$R(3K2,K1,n), for any n ≥ 3. Furthermore, by using computational approach, we determine all Ramsey $${(3K_2,K_{1,n})}$$(3K2,K1,n)-minimal graphs of order at most 10 vertices for $${3 \leq n \leq 7}$$3≤n≤7. We construct two classes of bipartite graphs in $${\mathcal{R}(3K_2,K_{1,n})}$$R(3K2,K1n), for any $${n \geq 3}$$n≥3. We also present a class of graphs containing a clique of six vertices in this set. We give large classes of graphs in the set $${\mathcal{R}(t K_2, K_{1,n})}$$R(tK2,K1,n), for $${n \geq 3}$$n≥3 and $${t \geq 4}$$t≥4, that are constructed from t disjoint stars.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Finite Ramsey set,Matching,Ramsey minimal graph,Star[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1007/s11786-015-0244-y[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]