Sep 4, 2020 · Thue's famous theorem says that every path is nonrepetitively 3-colourable. This paper surveys results about nonrepetitive colourings of graphs.

A coloring of the set of edges of a given graph G is non-repetitive if the sequence of colors on any path in. G is non-repetitive. We call the minimal number of ...

A coloring of the vertices of a graph G is nonrepetitive if there is no even path in G whose first half looks the same as the second half.

Mar 28, 2023 · In this paper, we focus on grids, which are the Cartesian products of paths. We prove that 5\le\pi(P_n\square P_n)\le12 for sufficiently large n ...

This idea combines graph colorings with Thue sequences introduced at the beginning of 20th century. In particular Thue proved that if G is a simple path of any ...

Oct 16, 2002 · A sequence a = a1a2 … an is said to be nonrepetitive if no two adjacent blocks of a are exactly the same. For instance, the sequence 1232321 ...

A vertex coloring of a graph G is k-nonrepetitive if one cannot find a periodic sequence with k blocks on any simple path of G. The minimum number of colors ...

In this paper we consider a natural generalization of Thue's sequences for colorings of graphs. A coloring of the set of edges of a given graph G is ...

A vertex coloring of a graph G is k-nonrepetitive if one cannot find a periodic sequence with k blocks on any simple path of G. The minimum number of colors ...

A coloring of the vertices of a graph G is nonrepetitive if no simple path in G looks like a 1 a 2 ... a n a 1 a 2 ... a n. The minimum number of colors ...