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Rao's degree sequence conjecture

โœ Scribed by Chudnovsky, Maria; Seymour, Paul


Book ID
125442696
Publisher
Elsevier Science
Year
2014
Tongue
English
Weight
548 KB
Volume
105
Category
Article
ISSN
0095-8956

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Rao's conjecture on self-complementary g
โœ Kiyoshi Ando ๐Ÿ“‚ Article ๐Ÿ“… 1985 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 106 KB

## Abstract Rao posed the following conjecture, โ€œLet G be a selfโ€complementary graph of order __p__, ฯ€ = (d~1~ โ€ฆ dp) be its degree sequence. Then G has a kโ€factor if and only if ฯ€ โˆ’ k, = (d1 โˆ’ k, โ€ฆ dP โˆ’ k) is graphical.โ€ We construct a family of counterexamples for this conjecture for every k โฉพ 3.