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- W3167236306 abstract "The Thue number $pi(G)$ of a graph $G$ is the minimum number of colors needed to color $G$ without creating a square on a path of $G$. For a graph class $C$, $pi(C)$ is the supremum of $pi(G)$ over the graphs $Gin C$. The Thue number has been investigated for famous minor-closed classes: $pi(tree)=4$, $7lepi(outerplanar)le12$, and $11lepi(planar)le768$. Following a suggestion of Grytczuk, we consider the generalized parameters $pi_k(C)$ such that only squares of period at least $k$ must be avoided. Thus, $pi(C)=pi_1(C)$. We show that $pi_5(tree)=2$, $pi_2(tree)=3$, and $pi_k(planar)ge11$ for every fixed $k$." @default.
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- W3167236306 date "2021-06-03" @default.
- W3167236306 modified "2023-09-27" @default.
- W3167236306 title "Avoiding large squares in trees and planar graphs" @default.
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