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• W4226343193 abstract "Abstract A nonnegative integer sequence is k -graphic if it is the degree sequence of a k -uniform simple hypergraph. The problem of deciding whether a given sequence $$pi $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>π</mml:mi> </mml:math> is 3-graphic has recently been proved to be NP-complete, after years of studies. Thus, it acquires primary relevance to detect classes of degree sequences whose graphicality can be tested in polynomial time in order to restrict the NP-hard core of the problem and design algorithms that can also be useful in different research areas. Several necessary and few sufficient conditions for $$pi $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>π</mml:mi> </mml:math> to be k -graphic, with $$kge 3$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> , appear in the literature. Frosini et al. defined a polynomial time algorithm to reconstruct k -uniform hypergraphs having regular or almost regular degree sequences. Our study fits in this research line providing a combinatorial characterization of span-two sequences, i.e., sequences of the form $$pi =(d,ldots ,d,d-1,ldots ,d-1,d-2,ldots ,d-2)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>π</mml:mi> <mml:mo>=</mml:mo> <mml:mo>(</mml:mo> <mml:mi>d</mml:mi> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:mi>d</mml:mi> <mml:mo>,</mml:mo> <mml:mi>d</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:mi>d</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>d</mml:mi> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:mi>d</mml:mi> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , $$dge 2$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , which are degree sequences of some 3-uniform hypergraphs. Then, we define a polynomial time algorithm to reconstruct one of the related 3-uniform hypergraphs. Our results are likely to be easily generalized to $$k ge 4$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> and to other families of degree sequences having simple characterization, such as gap-free sequences." @default.
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• W4226343193 date "2022-04-07" @default.
• W4226343193 modified "2023-09-26" @default.
• W4226343193 title "On the Reconstruction of 3-Uniform Hypergraphs from Degree Sequences of Span-Two" @default.
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• W4226343193 doi "https://doi.org/10.1007/s10851-022-01074-2" @default.
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