Restricted size Ramsey number for P 3 versus cycles
نویسندگان
چکیده
Let F , G and H be simple graphs. We say F → (G,H) if for every 2-coloring of the edges of F there exists a monochromatic G orH in F . The Ramsey number r(G,H) is defined as r(G,H) = min{|V (F )| : F → (G,H)}, while the restricted size Ramsey number r(G,H) is defined as r(G,H) = min{|E(F )| : F → (G,H), |V (F )| = r(G,H)}. In this paper we determine previously unknown restricted size Ramsey numbers r∗(P3, Cn) for 7 ≤ n ≤ 12. We also give new upper bound r∗(P3, Cn) ≤ 2n− 2 for even n ≥ 8.
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