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تسجيل مستخدم جديدLarge chromatic number and Ramsey graphs
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Let Q(n,c) denote the minimum clique size an n-vertex graph can have if its chromatic number is c. Using Ramsey graphs we give an exact, albeit implicit, formula for the case c is at least (n+3)/2.
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A signed graph is a pair $(G, sigma)$, where $G$ is a graph and $sigma: E(G) to {+, -}$ is a signature which assigns to each edge of $G$ a sign. Various notions of coloring of signed graphs have been studied. In this paper, we extend circular colorin
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Resolving a problem raised by Norin, we show that for each $k in mathbb{N}$, there exists an $f(k) le 7k$ such that every graph $G$ with chromatic number at least $f(k)+1$ contains a subgraph $H$ with both connectivity and chromatic number at least $
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By a finite type-graph we mean a graph whose set of vertices is the set of all $k$-subsets of $[n]={1,2,ldots, n}$ for some integers $nge kge 1$, and in which two such sets are adjacent if and only if they realise a certain order type specified in ad
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