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Connectivity of Cartesian Product of Hypergraphs
Bulletin of the Iranian Mathematical Society, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Na, Meng, Jixiang, Tian, Yingzhi
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American Journal of Mathematics, 1969
0. Introduction. Let as be an arc in the interior In of the n-cell In and let X be the quotient space I"/ac obtained by shrinking a to a point. According to Kwun and Raymond [4], X X 12 is an (n + 2)-cell. The crucial tool in their proof is the result of Andrews-Curtis that, under the above conditions, In/a X R1 is homeomorphic to In XR1.
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0. Introduction. Let as be an arc in the interior In of the n-cell In and let X be the quotient space I"/ac obtained by shrinking a to a point. According to Kwun and Raymond [4], X X 12 is an (n + 2)-cell. The crucial tool in their proof is the result of Andrews-Curtis that, under the above conditions, In/a X R1 is homeomorphic to In XR1.
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On the Discrepancy for Cartesian Products
Journal of the London Mathematical Society, 2000We prove that the discrepancy for the family of Cartesian products \(B_1\times B_2\subseteq \mathbb{R}^4\), where \(B_1\) and \(B_2\) are circular discs in the plane, is \(O(n^{1/4+\varepsilon})\) for an arbitrarily small constant \(\varepsilon>0\), i.e. essentially the same as that for discs in the plane.
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Radicals commuting with cartesian products
Archiv der Mathematik, 1998Given an Abelian group \(G\), the group radical is defined by \(R_G(X)=\bigcap\{\text{Ker }\phi\mid\phi\colon X\to G\}\), for Abelian groups \(X\). This radical does not always commute with infinite direct products (for instance, when \(G=\mathbb{Q}\), it turns into the torsion radical).
Corner, A. L. S., Göbel, Rüdiger
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1970
When we say in analytic geometry that a point has co-ordinates (x, y), the order in which x and y occur, in the symbol (x, y), is important: (1, 2) ≠ (2, 1). For this reason we call (x, y) an ordered pair. Moreover, x and y come from sets; in this case x, y ∈ R. This idea can be generalizedf as follows. Let 𝒰 be a universe.
H. B. Griffiths, P. J. Hilton
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When we say in analytic geometry that a point has co-ordinates (x, y), the order in which x and y occur, in the symbol (x, y), is important: (1, 2) ≠ (2, 1). For this reason we call (x, y) an ordered pair. Moreover, x and y come from sets; in this case x, y ∈ R. This idea can be generalizedf as follows. Let 𝒰 be a universe.
H. B. Griffiths, P. J. Hilton
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Homogeneous Cartesian products
Australas. J Comb., 2002Summary: A graph \(G\) is 1-homogeneous if certain isomorphisms between similarly embedded induced subgraphs of \(G\) extend to automorphisms of \(G\). We show that the only connected composite 1-homogeneous graphs are the cube, and \(K_n\times K_2\) and \(K_n\times K_n\) with \(n\geq 2\).
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Factoring cartesian‐product graphs
Journal of Graph Theory, 1994AbstractIn a fundamental paper, G. Sabidussi [“Graph Multiplication,” Mathematische Zeitschrift, Vol. 72 (1960), pp. 446–457] used a tower of equivalence relations on the edge set E(G) of a connected graph G to decompose G into a Cartesian product of prime graphs. Later, a method by R.L. Graham and P.M.
Imrich, Wilfried, Žerovnik, Janez
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On the Width of the Cartesian Product of Ordinals
OrderzbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Cartesian products of trees and paths
Journal of Graph Theory, 1996Let all graphs be connected and simple, not necessarily finite. A subgraph \(F\) of \(G\) is called isometric if any two vertices of \(F\) have the same distance in \(G\) as in \(F\); and the interval \(I(x,y)\) consists of all vertices on the shortest paths between \(x\) and \(y\).
Hans-Jürgen Bandelt +2 more
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On the skewness of Cartesian products with trees
Discrete Applied Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhangdong Ouyang +2 more
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