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arXiv · 1808.04540

A Ramsey-type theorem for the matching number regarding connected graphs

Ilkyoo Choi·Michitaka Furuya·Ringi Kim·Boram Park
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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.

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Ilkyoo Choi, Michitaka Furuya, Ringi Kim, Boram Park. 2018-08-14. A Ramsey-type theorem for the matching number regarding connected graphs. https://arxiv.org/abs/1808.04540

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