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In the article, the existence of rainbow cycles in edge colored plane triangulations is studied. It is shown that the minimum number of colors that force the existence of a rainbow C3 in any n‐vertex plane triangulation is equal to . For a lower bound and for an upper bound of the number is determined.
For a given graph $$H$$ H and $$n \ge 1,$$ n ≥ 1 , let $$f(n, H)$$ f ( n , H ) denote the maximum number $$m$$ m for which it is possible to colour the edges of the complete graph $$K_n$$ K n with $$m$$ m colours in such a way that each subgraph $$H$$ H in $$K_n$$ K n has at least two edges of the same colour. Equivalently,...
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