Nordhaus-Gaddum problems for Colin de Verdière type parameters, variants of tree-width, and related parameters

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2016-01-01
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Hogben, Leslie
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Electrical and Computer EngineeringMathematics
Abstract

A Nordhaus-Gaddum problem for a graph parameter is to determine a tight lower or upper bound for the sum or product of the parameter evaluated on a graph and on its complement. This article surveys Nordhaus-Gaddum results for the Colin de Verdiere type parameters mu, nu, and xi; tree-width and its variants largeur d'arborescence, path-width, and proper path-width; and minor monotone ceilings of vertex connectivity and minimum degree.

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This is a post-peer-review, pre-copyedit version of a book chapter published as Hogben, Leslie. "Nordhaus-Gaddum problems for Colin de Verdiere type parameters, variants of tree-width, and related parameters." In Beveridge A., Griggs J., Hogben L., Musiker G., Tetali P. (eds) Recent Trends in Combinatorics. The IMA Volumes in Mathematics and its Applications, vol. 159. Springer, Cham. (2016): 275-294. DOI: 10.1007/978-3-319-24298-9_12. Posted with permission.

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Fri Jan 01 00:00:00 UTC 2016
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