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Titlebook: Recent Trends in Combinatorics; Andrew Beveridge,Jerrold R. Griggs,Prasad Tetali Book 2016 Springer International Publishing Switzerland 2

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Mei-Chu Chang no more. Ex- cise testing, which providesinformationon tness, the risk of coronarydisease, and all around vitality, is now being performed in the of ces of primary care physicians across the United States. Although there is a signi cant risk in some populations, a careful doctor who takes the troub
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Repetitions in graphs and sequencess vertex-disjoint induced subgraphs of the same order and size, disjoint vertex sets with the same multiset of pairwise distances, subgraphs with the same maximum degree. This paper surveys results on unavoidable repetitions, also referred to as twins, with a focus on three asymptotically tight results obtained over the past 5 years.
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Giant components in random graphsts, random graphs on surfaces). The second trend is finding new simple proofs (and thereby improvement) of classical results on random graphs. This article discusses developments in random graphs in the light of these trends, with focus on giant components, limit theorems, and proof techniques.
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