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A direct proof and a generalization for a Kantorovich type inequality

✍ Scribed by Jianguo Huang; Jieyong Zhou

Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 204 KB
Volume: 397
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2004.10.009

No coin nor oath required. For personal study only.

✦ Synopsis

A direct proof for a Kantorovich type inequality due to Bauer and Householder is presented. A generalization of the inequality is also established by the theory of compound matrices.

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## Abstract For a simple graph of maximum degree Δ, it is always possible to color the edges with Δ + 1 colors (Vizing); furthermore, if the set of vertices of maximum degree is independent, Δ colors suffice (Fournier). In this article, we give a short constructive proof of an extension of these re