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Ramsey Graphs Induce Subgraphs of Many Different Sizes
• Mathematics, Computer Science
• Comb.
• 6 September 2016
A graph on n vertices is said to be C-Ramsey if every clique or independent set of the graph induces subgraphs of at least n2-o(1) distinct sizes. Expand
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Counting Zeros of Cosine Polynomials: On a Problem of Littlewood
We show that if $A$ is a finite set of non-negative integers then the number of zeros of the function $f_A(\theta) = \sum_{a \in A} \cos(a\theta),$ in $[0,2\pi]$, is at least $(\log \log \logExpand • 6 • 3 • PDF Dense subgraphs in random graphs • Mathematics, Computer Science • Discret. Appl. Math. • 27 March 2018 We show that$\omega_{\gamma}(G_{n,p})$is concentrated on a set of two integers. Expand • 6 • 2 • PDF A stability theorem for maximal Kr+1-free graphs • Mathematics, Computer Science • J. Comb. Theory, Ser. B • 16 August 2016 For$r \geq 2$, we show that every maximal$K_{r+1}$-free graph$G$on$n$vertices with$(1-\frac{1}{r})\frac{n^2}{2}-o(n^{\frac{r+ 1}{r}})$edges contains a complete$r$-partite subgraph on$(1 - o(1))n$. Expand • 2 • 2 • PDF Partitioning a graph into monochromatic connected subgraphs • Mathematics, Computer Science • J. Graph Theory • 3 August 2017 A well-known result by Haxell and Kohayakawa states that the vertices of an$r$-coloured complete graph can be partitioned into$r-1$monochromatic connected subgraphs of distinct colours; this is a slightly weaker variant of a conjecture by Erdős, Pyber and Gyarfas. Expand • 4 • 2 • PDF On Abelian and Additive Complexity in Infinite Words • Mathematics, Computer Science • Integers • 23 July 2011 In this note we define bounded additive complexity for infinite words over a finite subset of . Expand • 9 • 1 • PDF On the Maximum Running Time in Graph Bootstrap Percolation • Mathematics, Computer Science • Electron. J. Comb. • 24 October 2015 Graph bootstrap percolation is a simple cellular automaton introduced by Bollob\'as in 1968. Expand • 7 • 1 • PDF On a New Idiom in the Study of Entailment • R. Jennings, Yue Chen • Mathematics, Computer Science • Logica Universalis • 29 March 2011 This paper is an experiment in Leibnizian analysis. The reader will recall that Leibniz considered all true sentences to be analytically so. The difference, on his account, between necessary andExpand • 3 • PDF Central limit theorems from the roots of probability generating functions • Mathematics • 20 April 2018 For each$n$, let$X_n \in \{0,\ldots,n\}$be a random variable with mean$\mu_n$, standard deviation$\sigma_n$, and let $P_n(z) = \sum_{k=0}^n \mathbb{P}( X_n = k) z^k ,$ be its probabilityExpand • 6 • PDF Central limit theorems and the geometry of polynomials • Mathematics • 23 August 2019 Let$X \in \{0,\ldots,n \}$be a random variable, with mean$\mu$and standard deviation$\sigma\$ and let $f_X(z) = \sum_{k} \mathbb{P}(X = k) z^k,$ be its probability generating function.Expand
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