Restricted Size Ramsey Number Involving Matching and Graph of Order Five
نویسندگان
چکیده
منابع مشابه
Restricted size Ramsey number for path of order three versus graph of order five
Let G and H be simple graphs. The Ramsey number r(G,H) for a pair of graphs G and H is the smallest number r such that any red-blue coloring of the edges of Kr contains a red subgraph G or a blue subgraph H . The size Ramsey number r̂(G,H) for a pair of graphs G and H is the smallest number r̂ such that there exists a graph F with size r̂ satisfying the property that any red-blue coloring of the e...
متن کاملRestricted size Ramsey number for P 3 versus cycles
Let F , G and H be simple graphs. We say F → (G,H) if for every 2-coloring of the edges of F there exists a monochromatic G orH in F . The Ramsey number r(G,H) is defined as r(G,H) = min{|V (F )| : F → (G,H)}, while the restricted size Ramsey number r(G,H) is defined as r(G,H) = min{|E(F )| : F → (G,H), |V (F )| = r(G,H)}. In this paper we determine previously unknown restricted size Ramsey num...
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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...
متن کاملThe Size Ramsey Number
Let i2 denote the class of all graphs G which satisfy G-(Gl, GE). As a way of measuring r inimality for members of P, we define the Size Ramsey number ; We then investigate various questions concerned with the asymptotic behaviour of r .
متن کاملON THE MATCHING NUMBER OF AN UNCERTAIN GRAPH
Uncertain graphs are employed to describe graph models with indeterministicinformation that produced by human beings. This paper aims to study themaximum matching problem in uncertain graphs.The number of edges of a maximum matching in a graph is called matching numberof the graph. Due to the existence of uncertain edges, the matching number of an uncertain graph is essentially an uncertain var...
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ژورنال
عنوان ژورنال: Journal of Mathematical and Fundamental Sciences
سال: 2020
ISSN: 2338-5510,2337-5760
DOI: 10.5614/j.math.fund.sci.2020.52.2.1