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Global security in claw-free cubic graphs

✍ Scribed by Jesse-Józefczyk, Katarzyna; Sidorowicz, Elżbieta

Book ID: 124146922
Publisher: Elsevier Science
Year: 2014
Tongue: English
Weight: 543 KB
Volume: 175
Category: Article
ISSN: 0166-218X
DOI: 10.1016/j.dam.2014.05.027

No coin nor oath required. For personal study only.

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A graph is said to be claw-free if it does not contain an induced subgraph isomorphic to KI,3. Let k be a positive integer. Our main result is as follows: If G is a claw-free graph of order at least 3k and d(x) + d(y)>~3k + 1 for every pair of non-adjacent vertices x and y of G, then G contains k v