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Sharp bounds for sums associated to graphs of matrices

✍ Scribed by James A. Mingo; Roland Speicher


Book ID
113710213
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
235 KB
Volume
262
Category
Article
ISSN
0022-1236

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## Abstract We show that every 1‐tough graph __G__ on __n__ β‰₯ 3 vertices with Οƒ~3~≧ __n__ has a cycle of length at least min{__n, n__ + (Οƒ~3~/3 ) βˆ’ Ξ± + 1}, where Οƒ~3~ denotes the minimum value of the degree sum of any 3 pairwise nonadjacent vertices and Ξ± the cardinality of a miximum independent se