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The planar Ramsey number PR (H1, H2) is the smallest integer n such that any planar graph on n vertices contains a copy of H1 or its complement contains a copy of H2.
It is known that the Ramsey number R(K4 -e, K6)
= 21, and the planar Ramsey numbers PR(K4 - e, Kl)
for l ≤ 5 are known. In this paper,
we give the lower bounds on PR (K4 ? e, Kl) and determine
the exact value of PR (K4 - e, K6).