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- W4289694513 abstract "A major line of research is discovering Ramsey-type theorems, which are results of the following form: given a graph parameter $rho$, every graph $G$ with sufficiently large $rho(G)$ contains a `well-structured' induced subgraph $H$ with large $rho(H)$. The classical Ramsey's theorem deals with the case when the graph parameter under consideration is the number of vertices; there is also a Ramsey-type theorem regarding connected graphs. Given a graph $G$, the matching number and the induced matching number of $G$ is the maximum size of a matching and an induced matching, respectively, of $G$. In this paper, we formulate Ramsey-type theorems for the matching number and the induced matching number regarding connected graphs. Along the way, we obtain a Ramsey-type theorem for the independence number regarding connected graphs as well." @default.
- W4289694513 created "2022-08-04" @default.
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- W4289694513 date "2018-08-14" @default.
- W4289694513 modified "2023-10-03" @default.
- W4289694513 title "A Ramsey-type theorem for the matching number regarding connected graphs" @default.
- W4289694513 doi "https://doi.org/10.48550/arxiv.1808.04540" @default.
- W4289694513 hasPublicationYear "2018" @default.
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