# The Thickness of Amalgamations and Cartesian Product of Graphs

Discussiones Mathematicae Graph Theory (2017)

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

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topYan 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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