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COMBINATORICA, 1998
The induced Ramsey number \(r_{\text{ind}}(G,H)\), is the smallest possible order of a graph \(F\) with the property that if the edges of \(F\) are \(2\)-colored, there is an induced subgraph of \(G\) in the first color or \(H\) in the second color.
Yoshiharu Kohayakawa +2 more
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The induced Ramsey number \(r_{\text{ind}}(G,H)\), is the smallest possible order of a graph \(F\) with the property that if the edges of \(F\) are \(2\)-colored, there is an induced subgraph of \(G\) in the first color or \(H\) in the second color.
Yoshiharu Kohayakawa +2 more
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Graphs and Combinatorics, 1991
Denote by \(br(G;k)\) the \(k\)-color bipartite Ramsey number of a bipartite graph \(G\), i.e. the minimum integer \(n\) such that in any \(k\)-coloring of the edges of \(K_{n,n}\) there is a monochromatic subgraph isomorphic to \(G\). In this note the author proved that \(br(C_ 4;3)=11\).
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Denote by \(br(G;k)\) the \(k\)-color bipartite Ramsey number of a bipartite graph \(G\), i.e. the minimum integer \(n\) such that in any \(k\)-coloring of the edges of \(K_{n,n}\) there is a monochromatic subgraph isomorphic to \(G\). In this note the author proved that \(br(C_ 4;3)=11\).
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Doklady Mathematics, 2013
A graph is a distance graph in \(R^d,\) the \(d\)-dimension Euclidean space, if its vertices can be associated with different points of \(R^d\) such that any pair of adjacent vertices of such a graph corresponds to a pair of points a unit distance apart.
Kupavskii, A. B., Titova, M. V.
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A graph is a distance graph in \(R^d,\) the \(d\)-dimension Euclidean space, if its vertices can be associated with different points of \(R^d\) such that any pair of adjacent vertices of such a graph corresponds to a pair of points a unit distance apart.
Kupavskii, A. B., Titova, M. V.
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Ramsey and Gallai-Ramsey Numbers of Cycles and Books
Acta Mathematicae Applicatae Sinica, English SerieszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wei, Mei-qin +3 more
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Ars Comb., 2001
Summary: For a graph \(G\), a partiteness \(k \geq 2\) and a number of colours \(c\), we define the multipartite Ramsey number \(r^c_k(G)\) as the minimum value \(m\) such that, given any colouring using \(c\) colours of the edges of the complete balanced \(k\)-partite graph with \(m\) vertices in each partite set, there must exist a monochromatic copy
David P. Day +3 more
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Summary: For a graph \(G\), a partiteness \(k \geq 2\) and a number of colours \(c\), we define the multipartite Ramsey number \(r^c_k(G)\) as the minimum value \(m\) such that, given any colouring using \(c\) colours of the edges of the complete balanced \(k\)-partite graph with \(m\) vertices in each partite set, there must exist a monochromatic copy
David P. Day +3 more
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Lower bounds for multicolor Ramsey numbers
Advances in Mathematics, 2021David Conlon, Asaf Ferber
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On Ramsey and star-critical Ramsey numbers for generalized fans versus nKm
Discrete Applied Mathematics, 2021SUZANNA Thompson
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Discrete Applied Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Ramsey and Gallai–Ramsey numbers for the union of paths and stars
Discrete Applied Mathematics, 2023Yaping Mao
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Rainbow Generalizations of Ramsey Theory: A Survey
Graphs and Combinatorics, 2010Shinya Fujita +2 more
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