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Award ID contains: 1945481

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  1. ; (, Journal of Graph Theory)
    Abstract We present a refinement of the classical alteration method for constructing ‐free graphs for suitable edge‐probabilities , we show that removing all edges in ‐copies of the binomial random graph does not significantly change the independence number. This differs from earlier alteration approaches of Erdős and Krivelevich, who obtained similar guarantees by removing one edge from each ‐copy (instead of all of them). We demonstrate the usefulness of our refined alternation method via two applications to online graph Ramsey games, where it enables easier analysis. 
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  2. ; (, Random Structures & Algorithms)
    Abstract We consider rooted subgraphs in random graphs, that is, extension counts such as (i) the number of triangles containing a given vertex or (ii) the number of paths of length three connecting two given vertices. In 1989, Spencer gave sufficient conditions for the event that, with high probability, these extension counts are asymptotically equal for all choices of the root vertices. For the important strictly balanced case, Spencer also raised the fundamental question as to whether these conditions are necessary. We answer this question by a careful second moment argument, and discuss some intriguing problems that remain open. 
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  3. ; ; (, IEEE Transactions on Information Theory)
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  4. ; (, European Journal of Combinatorics)
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  5. ; (, The Annals of Applied Probability)
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  6. ; ; (, Discrete Mathematics)
    null (Ed.)
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