Universität zu Köln

Bachoc, Christine, DeCorte, Evan, de Oliveira Filho, Fernando Mario and Vallentin, Frank ORCID: 0000-0002-3205-4607 (2014). Spectral bounds for the independence ratio and the chromatic number of an operator. Isr. J. Math., 202 (1). S. 227 - 255. JERUSALEM: HEBREW UNIV MAGNES PRESS. ISSN 1565-8511

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Abstract

We define the independence ratio and the chromatic number for bounded, self-adjoint operators on an L (2)-space by extending the definitions for the adjacency matrix of finite graphs. In analogy to the Hoffman bounds for finite graphs, we give bounds for these parameters in terms of the numerical range of the operator. This provides a theoretical framework in which many packing and coloring problems for finite and infinite graphs can be conveniently studied with the help of harmonic analysis and convex optimization. The theory is applied to infinite geometric graphs on Euclidean space and on the unit sphere.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Bachoc, Christine UNSPECIFIED UNSPECIFIED UNSPECIFIED DeCorte, Evan UNSPECIFIED UNSPECIFIED UNSPECIFIED de Oliveira Filho, Fernando Mario UNSPECIFIED UNSPECIFIED UNSPECIFIED Vallentin, Frank UNSPECIFIED orcid.org/0000-0002-3205-4607 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-434228
DOI:	10.1007/s11856-014-1070-7
Journal or Publication Title:	Isr. J. Math.
Volume:	202
Number:	1
Page Range:	S. 227 - 255
Date:	2014
Publisher:	HEBREW UNIV MAGNES PRESS
Place of Publication:	JERUSALEM
ISSN:	1565-8511
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language DELSARTE Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/43422