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On Some Problems of Lovász Concerning the Shannon Capacity of a Graph

✍ Scribed by Haemers, W.


Book ID
111919739
Publisher
IEEE
Year
1979
Tongue
English
Weight
299 KB
Volume
25
Category
Article
ISSN
0018-9448

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On a Conjecture of Lovász Concerning Bri
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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 i

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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.