On types of growth for graph-different permutations
Journal of Combinatorial Theory Series A
Permutation Capacities of Families of Oriented Infinite Paths
SIAM Journal on Discrete Mathematics
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For a finite graph $G$ whose vertices are different natural numbers we call two infinite permutations of the natural numbers $G$-different if they have two adjacent vertices of $G$ somewhere in the same position. The maximum number of pairwise $G$-different permutations of the naturals is always finite. We study this maximum as a graph invariant and relate it to a problem of the first two authors on colliding permutations. An improvement on the lower bound for the maximum number of pairwise colliding permutations is obtained.