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We give a new and short proof of a theorem on k-hypertournament losing scores due to Zhou et al. [8].

Given non-negative integers n i and α i with 0 ≤ α i ≤ n i

For two given graphs G and H, the planar Ramsey number P R(G, H) is the smallest integer n such that every planar graph F on n vertices either contains a copy of G, or its complement contains a copy of H. In this paper, we determine all planar Ramsey numbers for a triangle versus wheels.

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