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

A major line of research is discovering Ramsey-type theorems, which are results of the following form: given a graph parameter ρ, every graph G with sufficiently large ρ(G) contains a particular induced subgraph H with large ρ(H). The classical Ramsey’s theorem deals with the case when the graph par...

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Bibliographic Details
Published in:Discrete mathematics 2020-02, Vol.343 (2), p.111648, Article 111648
Main Authors: Choi, Ilkyoo, Furuya, Michitaka, Kim, Ringi, Park, Boram
Format: Article
Language:English
Subjects:
Induced matching number
Matching number
Ramsey-type theorem
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Summary:A major line of research is discovering Ramsey-type theorems, which are results of the following form: given a graph parameter ρ, every graph G with sufficiently large ρ(G) contains a particular induced subgraph H with large ρ(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, namely, every sufficiently large connected graph contains a large induced connected graph that is a complete graph, a large star, or a path. Given a graph G, the matching number and the induced matching number of G are 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.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2019.111648