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We say that a coloring of R2 is line k-nonrepetitive if we will never encounter the same sequence of colors k times in a row when going along any straight line with steps of length 1 unit. This notion is closely related to square- and cube-free words, introduced by Thue.We show that there exists a line 40-nonrepetitive coloring of the plane with only 2 colors. Moreover, we generalize this result for...
In this paper we give an algorithm for counting the number of all independent sets in a claw-free graph which works in time O*(1.08352n) for graphs with no vertices of degree larger than 3 and O*(1.23544n) for arbitrary claw-free graphs, where n is the number of vertices in the instance graph.
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