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Approximating Longest Cycles in Graphs with Bounded Degrees

โœ Scribed by Chen, Guantao; Gao, Zhicheng; Yu, Xingxing; Zang, Wenan


Book ID
118180686
Publisher
Society for Industrial and Applied Mathematics
Year
2006
Tongue
English
Weight
301 KB
Volume
36
Category
Article
ISSN
0097-5397

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We show that every graph G on n vertices with minimal degree at least n / k contains a cycle of length at least [ n / ( k -111. This verifies a conjecture of Katchalski. When k = 2 our result reduces t o the classical theorem of Dirac that asserts that if all degrees are at least i n then G is Hamil