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arXiv · 1201.6483

The thickness of amalgamations of graphs

Yan Yang·Xiangheng Kong
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Abstract

The thickness $θ(G)$ of a graph $G$ is the minimum number of planar spanning subgraphs into which the graph $G$ can be decomposed. As a topological invariant of a graph, it is a measurement of the closeness to planarity of a graph, and it also has important applications to VLSI design. In this paper, the thickness of graphs that are obtained by vertex-amalgamation and bar-amalgamation of any two graphs whose thicknesses are known are obtained, respectively. And the lower and upper bounds for the thickness of graphs that are obtained by edge-amalgamation and 2-vertex-amalgamation of any two graphs whose thicknesses are known are also derived, respectively.

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Yan Yang, Xiangheng Kong. 2012-01-31. The thickness of amalgamations of graphs. https://arxiv.org/abs/1201.6483

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