### The coordinatewise uniformly Kadec-Klee property in some Banach spaces.

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Estimation of the Jung constants of Orlicz sequence spaces equipped with either the Luxemburg norm or the Orlicz norm is given. The exact values of the Jung constants of a class of reflexive Orlicz sequence spaces are found by using new quantitative indices for 𝓝-functions.

A spanning subgraph F of a graph G is called a P≥3-factor of G if every component of F is a path of order at least 3. A graph G is called a P≥3-factor covered graph if G has a P≥3-factor including e for any e ∈ E(G). In this paper, we obtain three sufficient conditions for graphs to be P≥3-factor covered graphs. Furthermore, it is shown that the results are sharp.

It is proved that if a Kothe sequence space $X$ is monotone complete and has the weakly convergent sequence coefficient WCS$\left(X\right)>1$, then $X$ is order continuous. It is shown that a weakly sequentially complete Kothe sequence space $X$ is compactly locally uniformly rotund if and only if the norm in $X$ is equi-absolutely continuous. The dual of the product space ${\left({\u2a01}_{i=1}^{\infty}{X}_{i}\right)}_{\Phi}$ of a sequence of Banach spaces ${\left({X}_{i}\right)}_{i=1}^{\infty}$, which is built by using an Orlicz function $\Phi $ satisfying the ${\Delta}_{2}$-condition, is computed isometrically (i.e. the exact...

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