# The Thickness of Amalgamations and Cartesian Product of Graphs

• Volume: 37, Issue: 3, page 561-572
• ISSN: 2083-5892

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## Abstract

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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.

## How to cite

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Yan Yang, and Yichao Chen. "The Thickness of Amalgamations and Cartesian Product of Graphs." Discussiones Mathematicae Graph Theory 37.3 (2017): 561-572. <http://eudml.org/doc/288484>.

@article{YanYang2017,
abstract = {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.},
author = {Yan Yang, Yichao Chen},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {thickness; amalgamation; Cartesian product; genus},
language = {eng},
number = {3},
pages = {561-572},
title = {The Thickness of Amalgamations and Cartesian Product of Graphs},
url = {http://eudml.org/doc/288484},
volume = {37},
year = {2017},
}

TY - JOUR
AU - Yan Yang
AU - Yichao Chen
TI - The Thickness of Amalgamations and Cartesian Product of Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2017
VL - 37
IS - 3
SP - 561
EP - 572
AB - 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.
LA - eng
KW - thickness; amalgamation; Cartesian product; genus
UR - http://eudml.org/doc/288484
ER -

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