@article{edb786db4be14454b39cec69a29b79b8,

title = "Eigenvalue location in graphs of small clique-width",

abstract = "Finding a diagonal matrix congruent to A−cI for constants c, where A is the adjacency matrix of a graph G allows us to quickly tell the number of eigenvalues in a given interval. If G has clique-width k and a corresponding k-expression is known, then diagonalization can be done in time O(poly(k)n) where n is the order of G.",

author = "Martin F{\"u}rer and Carlos Hoppen and Jacobs, {David P.} and Vilmar Trevisan",

note = "Funding Information: Work supported by Science without Borders CNPq – Grant 400122/2014-6 , Brazil. M. F{\"u}rer acknowledges the support of NSF Grant CCF-1320814 . C. Hoppen thanks CNPq (Proj. 308539/2015-0 ) for their support. V. Trevisan acknowledges partial support of CNPq grants 409746/2016-9 and 303334/2016-9 , MATHAMSUD 18-MATH-01 and FAPERGS (Proj. PqG 17/2551-0001 ). Funding Information: Work supported by Science without Borders CNPq – Grant 400122/2014-6, Brazil. M. F{\"u}rer acknowledges the support of NSF Grant CCF-1320814. C. Hoppen thanks CNPq (Proj. 308539/2015-0) for their support. V. Trevisan acknowledges partial support of CNPq grants 409746/2016-9 and 303334/2016-9, MATHAMSUD 18-MATH-01 and FAPERGS (Proj. PqG 17/2551-0001). Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2019",

month = jan,

day = "1",

doi = "10.1016/j.laa.2018.09.015",

language = "English (US)",

volume = "560",

pages = "56--85",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

}