Note on the Multicolour Size-Ramsey Number for Paths,
نویسندگان
چکیده
منابع مشابه
The Size-ramsey Number
The size-Ramsey number of a graph G is the smallest number of edges in a graph Γ with the Ramsey property for G, that is, with the property that any colouring of the edges of Γ with two colours (say) contains a monochromatic copy of G. The study of size-Ramsey numbers was proposed by Erdős, Faudree, Rousseau, and Schelp in 1978, when they investigated the size-Ramsey number of certain classes o...
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متن کاملThe Multicolour Ramsey Number of a Long Odd Cycle
For a graph G, the k-colour Ramsey number Rk(G) is the least integer N such that every k-colouring of the edges of the complete graph KN contains a monochromatic copy of G. Bondy and Erdős conjectured that for an odd cycle Cn on n > 3 vertices, Rk(Cn) = 2 k−1(n− 1) + 1. This is known to hold when k = 2 and n > 3, and when k = 3 and n is large. We show that this conjecture holds asymptotically f...
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The size-Ramsey number of a graph G is the minimum number of edges in a graph H such that every 2-edge-coloring of H yields a monochromatic copy of G. Size-Ramsey numbers of graphs have been studied for almost 40 years with particular focus on the case of trees and bounded degree graphs. We initiate the study of size-Ramsey numbers for k-uniform hypergraphs. Analogous to the graph case, we cons...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2018
ISSN: 1077-8926
DOI: 10.37236/7954