Limits and Structures in Graph Theory

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• LALE ÖZKAHYA

We prove that $ \mathop{ \lim \inf}\limits_{n \rightarrow \infty} \frac{p_{n+1}-p_{n}}{\sqrt{\log p_{n}} \left(\log \log p_{n}\right)^{2}}< \infty, $where pn denotes the nth prime. Since on average pn+1−pn is asymptotically log n, this shows that we can always find pairs of primes much closer together than the average…

• CEM YALÇIN YILDIRIM

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• LALE ÖZKAHYA

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• AYÇA ÇEŞMELİOĞLU GÜL

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• EMİNE ŞULE YAZICI YURET

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For weakly regular bent functions in odd characteristic the dual function is also bent.We analyse a recently introduced construction of non-weakly regular bent functions andshow conditions under which their dual is bent as well. This leads to the definition ofthe class of dual-bent functions containing the class of we…

• AYÇA ÇEŞMELİOĞLU GÜL

The enumeration of independent sets in graphs with various restrictions has been a topic of much interest of late. Let $i(G)$ be the number of independent sets in a graph $G$ and let $i_t(G)$ be the number of independent sets in $G$ of size $t$. Kahn used entropy to show that if $G$ is an $r$-regular bipartite graph w…

Bent functions can be classified into regular bent functions, weakly regular but not regular bent functions, and non-weakly regular bent functions. Regular and weakly regular bent functions always appear in pairs, since their duals are also bent functions. In general, this does not apply to non-weakly regular bent fun…

• AYÇA ÇEŞMELİOĞLU GÜL

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• TINAZ EKİM

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It is shown that the size of a subgraph of Q n without a cycle of length 14 is of order o (| E ( Q n )|).

• LALE ÖZKAHYA