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Total weight choosability of graphs: Towards the 1-2-3-conjecture

Journal of Combinatorial Theory, Series B, 2021
The 1-2-3 conjecture states that for every simple graph with no isolated edges (a ``nice'' graph), one can assign weights of 1, 2, or 3 to each edge in such a way that all adjacent pairs of vertices have different total weights of incident edges. Although the conjecture was posed by \textit{M. Karoński} et al. [J. Comb. Theory, Ser. B 91, No.
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The 1‐2‐3‐conjecture holds for dense graphs

Journal of Graph Theory, 2018
AbstractThis paper confirms the 1‐2‐3‐conjecture for graphs that can be edge‐decomposed into cliques of order at least 3. Furthermore we combine this with a result by Barber, Kühn, Lo, and Osthus to show that there is a constants such that every graph with and , where is the minimum degree of satisfying the 1‐2‐3‐conjecture.
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Solving \(X^{2^{3n} + 2^{2n} + 2^n - 1} + (X + 1)^{2^{3n} + 2^{2n} + 2^n - 1} = b\) in \(\mathbb{F}_{2^{4 n}}\) and an alternative proof of a conjecture on the differential spectrum of the related monomial functions

2022
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Kim, Kwang Ho, Mesnager, Sihem
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The abc conjecture, as easy as 1, 2, 3 … or not

2012
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