Sierpiński r-一致超图的乘积

Art Discret. Appl. Math. Pub Date : 2021-03-17 DOI:10.26493/2590-9770.1402.D50

Mark Budden, Josh Hiller

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引用次数: 0

摘要

如果H1和H2是r-一致超图，f是V(H1)到V(H2)的所有(r−1)元素子集集合的函数，则Sierpinski积H1⊗fH2定义为具有顶点集V(H1) × V(H2)和超边分为两类:(g, H1) (g, H2)⋯(g, hr)，使得g∈V(H1)和h1h2⋯hr∈E(H2)，以及(g1, f({g1, g3，…，gr}))(g2, f({g1, g3，…，gr}))⋯(gr, f({g1, g2，…，gr−1}))，使得g1g2⋯gr∈E(H1)。我们开发了该产品所具有的基本结构，并提供了涉及连通性，团数和强色数的许多极值性质的证明。

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Sierpiński products of r-uniform hypergraphs

If H1 and H2 are r-uniform hypergraphs and f is a function from the set of all (r − 1)-element subsets of V(H1) into V(H2), then the Sierpinski product H1⊗fH2 is defined to have vertex set V(H1) × V(H2) and hyperedges falling into two classes: (g, h1)(g, h2)⋯(g, hr), such that g ∈ V(H1) and h1h2⋯hr ∈ E(H2),and (g1, f({g2, g3, …, gr}))(g2, f({g1, g3, …, gr}))⋯(gr, f({g1, g2, …, gr − 1})),such that g1g2⋯gr ∈ E(H1). We develop the basic structure possessed by this product and offer proofs of numerous extremal properties involving connectivity, clique numbers, and strong chromatic numbers.

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Art Discret. Appl. Math.

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