On Ramsey \((mK_2,H)\) -Minimal Graphs

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• 作者：Kristiana Wijaya ; Edy Tri Baskoro ; Hilda Assiyatun…
• 关键词：Ramsey minimal graph ; Edge coloring ; Matching ; Path ; Subdivision
• 刊名：Graphs and Combinatorics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：33
• 期：1
• 页码：233-243
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Combinatorics; Engineering Design;
• 出版者：Springer Japan
• ISSN：1435-5914
• 卷排序：33

文摘

Let \(\mathcal {R}(G,H)\) denote the set of all graphs F satisfying \(F \rightarrow (G,H)\) and for every \(e \in E(F),\)\((F-e) \nrightarrow (G,H).\) In this paper, we derive the necessary and sufficient conditions for graphs belonging to \(\mathcal {R}(mK_2,H)\) for any graph H and each positive integer m. We give all disconnected graphs in \(\mathcal {R}(mK_2,H),\) for any connected graph H. Furthermore, we prove that if \(F \in \mathcal {R}(mK_2,P_3),\) then any graph obtained by subdividing one non-pendant edge in F will be in \(\mathcal {R}((m+1)K_2,P_3)\).