| Abstract |
In 1966 T. Gallai asked do all longest paths meet?. Very soon, Walther answerd this question by presenting a counter example, a planar graph of 25 vertices. In last 50 years many variants of this problem appeared and some of them received positive answers but still a sufficient number of unsolved problems exist. Here, I will present a brief history of Gallai’s and related problems and and some possible ways to solve unsolved problems.
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