The Thickness of Amalgamations and Cartesian Product of Graphs

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 thickn...

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Main Authors:	Yang Yan, Chen Yichao
Format:	Article
Language:	English
Published:	Sciendo 2017-08-01
Series:	Discussiones Mathematicae Graph Theory
Subjects:	thickness amalgamation cartesian product genus 05c10
Online Access:	https://doi.org/10.7151/dmgt.1942

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spelling	doaj-06768ebca65e47ed8e0b349cea07e5172021-09-05T17:20:22ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922017-08-0137356157210.7151/dmgt.1942dmgt.1942The Thickness of Amalgamations and Cartesian Product of GraphsYang Yan0Chen Yichao1Department of Mathematics, Tianjin University, 300072, Tianjin, ChinaCollege of Mathematics and Econometrics, Hunan University, 410082Changsha, ChinaThe 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.https://doi.org/10.7151/dmgt.1942thicknessamalgamationcartesian productgenus05c10
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yang Yan Chen Yichao
spellingShingle	Yang Yan Chen Yichao The Thickness of Amalgamations and Cartesian Product of Graphs Discussiones Mathematicae Graph Theory thickness amalgamation cartesian product genus 05c10
author_facet	Yang Yan Chen Yichao
author_sort	Yang Yan
title	The Thickness of Amalgamations and Cartesian Product of Graphs
title_short	The Thickness of Amalgamations and Cartesian Product of Graphs
title_full	The Thickness of Amalgamations and Cartesian Product of Graphs
title_fullStr	The Thickness of Amalgamations and Cartesian Product of Graphs
title_full_unstemmed	The Thickness of Amalgamations and Cartesian Product of Graphs
title_sort	thickness of amalgamations and cartesian product of graphs
publisher	Sciendo
series	Discussiones Mathematicae Graph Theory
issn	2083-5892
publishDate	2017-08-01
description	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.
topic	thickness amalgamation cartesian product genus 05c10
url	https://doi.org/10.7151/dmgt.1942
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The Thickness of Amalgamations and Cartesian Product of Graphs

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