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.
@article{bwmeta1.element.doi-10_7151_dmgt_1942,
author = {Yan Yang and Yichao Chen},
title = {The Thickness of Amalgamations and Cartesian Product of Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {561-572},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1942}
}
Yan Yang; Yichao Chen. The Thickness of Amalgamations and Cartesian Product of Graphs. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 561-572. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1942/