Treewidth of the Line Graph of Complete and Complete Multipartite Graphs
Daniel J. Harvey, David R. Wood
TL;DR
This paper precisely calculates the treewidth of line graphs of complete and complete multipartite graphs, extending previous work and providing exact values or bounds for these graph classes.
Contribution
It determines the exact treewidth of line graphs of complete graphs and regular complete multipartite graphs, and bounds for arbitrary multipartite graphs.
Findings
Exact treewidth of line graph of complete graph
Exact treewidth of line graph of regular complete multipartite graph
Bounds for treewidth of line graph of arbitrary complete multipartite graph
Abstract
In recent papers by Grohe and Marx, the treewidth of the line graph of the complete graph is a critical example. We determine the exact treewidth of the line graph of the complete graph. By extending these techniques, we determine the exact treewidth of the line graph of a regular complete multipartite graph. For an arbitrary complete multipartite graph, we determine the treewidth of the line graph up to a lower order term.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Interconnection Networks and Systems