1. Star-Critical Ramsey Numbers of Cycles Versus Wheels.
- Author
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Liu, Yuchen and Chen, Yaojun
- Subjects
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RAMSEY numbers , *WHEELS , *INTEGERS - Abstract
For two graphs G 1 and G 2 , the star-critical Ramsey number r ∗ (G 1 , G 2) is the minimum integer k such that any red/blue edge-coloring of K r - 1 ⊔ K 1 , k contains a red copy of G 1 or a blue copy of G 2 , where r is the classical Ramsey number R (G 1 , G 2) and K r - 1 ⊔ K 1 , k is the graph obtained from a K r - 1 and an additional vertex v by joining v to k vertices of K r - 1 . Let C n denote a cycle of order n and W m a wheel of order m + 1 . Hook (2010) proved that r ∗ (C n , W 3) = 2 n for n ≥ 5 . In this paper, it is shown that r ∗ (C n , W m) = 2 n for m odd, n ≥ m ≥ 5 and n ≥ 60 . [ABSTRACT FROM AUTHOR]
- Published
- 2021
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