Set and size multipartite Ramsey numbers for stars

The set multipartite Ramsey number for stars Ms(K1,n1,…,K1,nk) is the smallest positive integer c such that any k-coloring of the edges of Kc×s contains a monochromatic star K1,ni in color i for some i, 1≤i≤k, where Kc×s denotes the complete multipartite graph having c classes with s vertices per ea...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 250; pp. 368 - 372
Main Authors Perondi, Pablo H., Monte Carmelo, Emerson L.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 11.12.2018
Elsevier BV
Subjects
Apexes
Applied mathematics
Chromatic index
Color
Coloring
Generalized Ramsey number
Graph theory
Multipartite graph
Number theory
Star
Stars
Multipartite graph
Star
Chromatic index
Generalized Ramsey number
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Summary:The set multipartite Ramsey number for stars Ms(K1,n1,…,K1,nk) is the smallest positive integer c such that any k-coloring of the edges of Kc×s contains a monochromatic star K1,ni in color i for some i, 1≤i≤k, where Kc×s denotes the complete multipartite graph having c classes with s vertices per each class. On the other hand, the size multipartite Ramsey number for stars, denoted by mc(K1,n1,…,K1,nk), is the smallest positive integer s such that any k-coloring of the edges of Kc×s contains a monochromatic copy of K1,ni in color i for some i, 1≤i≤k. In this note we compute both Ms(K1,n1,…,K1,nk) and mc(K1,n1,…,K1,nk), extending well-known results on the classical and the bipartite Ramsey numbers for stars, respectively.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2018.05.016