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Graphs and Combinatorics, 2023
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Mohammed A. Mutar +2 more
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Mohammed A. Mutar +2 more
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Journal of Graph Theory, 1978
AbstractFor n = 1, 2, …, let Bn = K2 + K̄n. We pose the problem of determining the Ramsey numbers r(Bm, Bn) and demonstrate that in many cases critical colorings are avialable from known examples of strongly regular graphs.
Cecil C. Rousseau, J. Sheehan
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AbstractFor n = 1, 2, …, let Bn = K2 + K̄n. We pose the problem of determining the Ramsey numbers r(Bm, Bn) and demonstrate that in many cases critical colorings are avialable from known examples of strongly regular graphs.
Cecil C. Rousseau, J. Sheehan
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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 C Maclennan
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Discrete Applied Mathematics
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