Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/17120
 Title: Spectral bounds for the k-regular induced subgraph problem Author: Cardoso, Domingos MoreiraPinheiro, Sofia J. Keywords: Spectral graph theoryMaximum k-regular induced subgraphsCombinatorial optimization Issue Date: Mar-2017 Publisher: Springer Abstract: Many optimization problems on graphs are reduced to the determination of a subset of vertices of maximum cardinality which induces a $k$-regular subgraph. For example, a maximum independent set, a maximum induced matching and a maximum clique is a maximum cardinality $0$-regular, $1$-regular and $(\omega(G)-1)$-regular induced subgraph, respectively, were $\omega(G)$ denotes the clique number of the graph $G$. The determination of the order of a $k$-regular induced subgraph of highest order is in general an NP-hard problem. This paper is devoted to the study of spectral upper bounds on the order of these subgraphs which are determined in polynomial time and in many cases are good approximations of the respective optimal solutions. The introduced upper bounds are deduced based on adjacency, Laplacian and signless Laplacian spectra. Some analytical comparisons between them are presented. Finally, all of the studied upper bounds are tested and compared through several computational experiments. URI: http://hdl.handle.net/10773/17120 DOI: 10.1007/978-3-319-49984-0_7 ISBN: 978-3-319-49982-6 Appears in Collections: CIDMA - Capítulo de livroOGTCG - Capítulo de livro

Files in This Item:
File Description SizeFormat