I am solving the example on Hamiltonian graphs:
We have 3 players of unique a game, there are 57 special cards. We know that by the rules of the game we can play only react to one card by 30 cards. At the start of the game every player has received 19 cards. The game is played in clockwise manner a -> b-> c ->a. When the player has no card he can play as reaction to previous card, he drops out. We also know that the card relations are symmetrical ( A -> B then we can play B -> A ).
Is it possible for person who knows the rules to create such shuffle of the cards that game will end on 19th turn with no dropout players ?
I deduced from it that the graph has $57$ vertices and $30$ nodes. Is this deduction correct? How to go from there?
There is a Hamiltonian path in every 57 vertex 30-regular graph. See Dirac's Theorem.