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On a Conjecture of Lovász Concerning Bricks: I. The Characteristic of a Matching Covered Graph

✍ Scribed by Marcelo H. de Carvalho; Cláudio L. Lucchesi; U.S.R. Murty

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 292 KB
Volume: 85
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.2001.2091

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✦ Synopsis

In 1987, Lova ´sz conjectured that every brick G different from K 4 , C ¯6, and the Petersen graph has an edge e such that G -e is a matching covered graph with exactly one brick. Lova ´sz and Vempala announced a proof of this conjecture in 1994. Their paper is under preparation. In this paper and its sequel (M. H.

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On a Conjecture of Lovász Concerning Bri

On a Conjecture of Lovász Concerning Bricks: II. Bricks of Finite Characteristic

✍ Marcelo H. de Carvalho; Cláudio L. Lucchesi; U.S.R. Murty 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 271 KB

we established the validity of the main theorem (1.1) for solid bricks. Here, we establish the existence of suitable separating cuts in nonsolid bricks and prove the theorem by applying induction to cut-contractions with respect to such cuts.