The study of the degree sequences of k-uniform hypergraphs, usually called k-sequences, has been a longstanding open problem for the case of $k>2$, and the corresponding decision version was proved to be NP-complete recently in 2018 [15]. The problem can be formalized as follows: Given a non decreasing sequence of positive integers $\pi =(d_1,d_2,\dots ,d_n)$, can π be the degree sequence of a k-uniform simple hypergraph? If the answer is positive, then the sequence π is said to be k-graphic. For $k=2$, that is for simple graphs, Erdös and Gallai [16] provided a characterization of the sequences that are 2-graphic (or simply, graphic). From this characterization, a polynomial time algorithm can be designed to reconstruct the incidence matrix of a graph having a given π as degree sequence (provided this graph exists). Due to the result of [15] and assuming $P\ne NP$, an efficiently computable characterization like the one for $k=2$ does not even exist for the case of 3-uniform hypergraphs.

Necessary or sufficient conditions for π to be k-graphic ($k\ge 3$) can be found in the literature. In this paper we prove some different new conditions: first we provide sufficient and also necessary conditions for the case of k-uniform and (almost) regular hypergraphs. Then, for $k=3$, we prove sufficient conditions in the case where π can be decomposed into ${\pi }^{\prime }$ and ${\pi }^{″}$, and ${\pi }^{\prime }$ is graphic.

Most of the results are obtained by borrowing tools from discrete tomography, a current research field on discrete mathematics.

对于k-一致超图的度数序列（通常称为k-序列）的研究一直是一个长期存在的开放问题。$ķ>\mathrm{2个}$，并且相应的决策版本最近被证明是NP-于2018年完成[15]。可以将问题形式化如下：给定正整数的非递减序列$\pi =（d_{\mathrm{1个}}，d_{\mathrm{2个}}，\dots ，d_{ñ}）$，π可以是k均匀简单超图的次数序列吗？如果答案是肯定的，则将序列π称为k图形。为了$ķ=\mathrm{2个}$，即对于简单图形，Erdös和Gallai [16]提供了2图形（或简单图形）序列的表征。根据该特征，可以设计多项式时间算法来重构具有给定π作为度数序列的图的入射矩阵（前提是存在该图）。由于[15]的结果，并假设$P\ne ñP$，一种高效的可计算特征，例如 $ķ=\mathrm{2个}$ 3均匀超图的情况甚至不存在。

π为k图形的必要或充分条件（$ķ\ge 3$）可以在文献中找到。在本文中，我们证明了一些不同的新条件：首先，我们为k一致和（几乎）正则超图的情况提供了充分必要的条件。然后，对于$ķ=3$，我们证明了在π可以分解为的情况下的充分条件${\pi }^{\prime }$ 和 ${\pi }^{\text{'}\text{'}}$， 和 ${\pi }^{\prime }$ 是图形的。

大多数结果是通过借用离散层析成像工具获得的，离散层析成像是当前对离散数学的研究领域。