Treewidth of the Line Graph of Complete and Complete Multipartite Graphs

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.

arXiv comment25 pages, 0 figures. Changes in this revision: One minor error fixed, substantial clean-up of text, title changed. A subset of this paper containing the first Theorem and its proof has been published in the Journal of Graph Theory: Harvey, D. J. and Wood, D. R. (2014), Treewidth of the Line Graph of a Complete Graph. J. Graph Theory. doi: 10.1002/jgt.21813