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Graphs and Combinatorics, 2023
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Mutar, Mohammed A. +2 more
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Mutar, Mohammed A. +2 more
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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.
Kohayakawa, Yoshiharu +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.
Kohayakawa, Yoshiharu +2 more
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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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2005
Sequences Bn(p,q) of connected parts of Euclidean and hyperbolic (p,q)-mosaic graphs are considered. The smallest n such that any 2-coloring of the edges of Bn( p,q) contains a given monochromatic graph G is introduced as gameboard Ramsey number rp,q(G). For p ≥ 4 it is proved that these Ramsey numbers exist for finitely many graphs only.
Bode, Jens-Peter, Harborth, Heiko
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Sequences Bn(p,q) of connected parts of Euclidean and hyperbolic (p,q)-mosaic graphs are considered. The smallest n such that any 2-coloring of the edges of Bn( p,q) contains a given monochromatic graph G is introduced as gameboard Ramsey number rp,q(G). For p ≥ 4 it is proved that these Ramsey numbers exist for finitely many graphs only.
Bode, Jens-Peter, Harborth, Heiko
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Graphs and Combinatorics, 2023
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Canonical Pattern Ramsey Numbers
Graphs and Combinatorics, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Axenovich, Maria, Jamison, Robert E.
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1998
Abstract The (diagonal) Ramsey number r(G) of a single graph G is the Ramsey number r(G, G). On pages 374—379 we depict all isolate-free graphs with up to 7 edges, with their Ramsey numbers. The R-number appearing in each top-right comer is the serial number of the graph in Burr’s catalogue; a graph that appears elsewhere in this Atlas ...
Ronald C Read, Robin J Wilson
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Abstract The (diagonal) Ramsey number r(G) of a single graph G is the Ramsey number r(G, G). On pages 374—379 we depict all isolate-free graphs with up to 7 edges, with their Ramsey numbers. The R-number appearing in each top-right comer is the serial number of the graph in Burr’s catalogue; a graph that appears elsewhere in this Atlas ...
Ronald C Read, Robin J Wilson
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Mixed Ramsey Numbers Revisited
Combinatorics, Probability and Computing, 2003Given a graph Hwith no isolates, the (generalized) mixed Ramsey number is the smallest integer r such that every H-free graph of order r contains an m-element irredundant set. We consider some questions concerning the asymptotic behaviour of this number (i) with H fixed and , (ii) with m fixed and a sequence of dense graphs, in particular for the ...
Rousseau, C. C., Speed, S. E.
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Journal of Graph Theory, 1978
AbstractA graph G is co‐connected if both G and its complement Ḡ are connected and nontrivial. For two graphs A and B, the connected Ramsey number rc(A, B) is the smallest integer n such that there exists a co‐connected graph of order n, and if G is a co‐connected graph on at least n vertices, then A ⩽ G or B ⩽ Ḡ.
Faudree, R. J., Schelp, R. H.
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AbstractA graph G is co‐connected if both G and its complement Ḡ are connected and nontrivial. For two graphs A and B, the connected Ramsey number rc(A, B) is the smallest integer n such that there exists a co‐connected graph of order n, and if G is a co‐connected graph on at least n vertices, then A ⩽ G or B ⩽ Ḡ.
Faudree, R. J., Schelp, R. H.
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Discrete Applied Mathematics
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