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The Thickness of Amalgamations and Cartesian Product of Graphs

100%

Yang Y., Chen Y.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 3

561-572

The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study the thickness of Cartesian product of graphs, and by using operations on graphs, we derive the thickness of the Cartesian product Kn □ Pm for most values of m and n.

Discrete thickness

75%

Scholtes S.

Molecular Based Mathematical Biology

2014

tom 2

nr 1

We investigate the relationship between a discrete version of thickness and its smooth counterpart. These discrete energies are deffned on equilateral polygons with n vertices. It will turn out that the smooth ropelength, which is the scale invariant quotient of length divided by thickness, is the Γ-limit of the discrete ropelength for n → ∞, regarding the topology induced by the Sobolev norm ‖ · ‖ W1,∞(S1,ℝd). This result directly implies the convergence of almost minimizers of the discrete energies in a fixed knot class to minimizers of the smooth energy.Moreover,we show that the unique absolute minimizer of inverse discrete thickness is the regular n-gon.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Molecular Based Mathematical Biology

1 Chen Y.

1 Scholtes S.

1 Yang Y.

1 2017

1 2014

Wyniki wyszukiwania

The Thickness of Amalgamations and Cartesian Product of Graphs

Discrete thickness