3 citations · 9 across the 16 of their papers we have counts for
9 papers · 1 filter
Ann wins the nonrepetitive game over four letters and the erase-repetition game over six letters
Matthieu Rosenfeld
We consider two games between two players Ann and Ben who build a word together by adding alternatively a letter at the end of the shared word. In the nonrepetitive game, Ben wins…
Avoiding large squares in trees and planar graphs
Daniel Gonçalves, Pascal Ochem, Matthieu Rosenfeld
The Thue number of a graph is the minimum number of colors needed to color without creating a square on a path of . For a graph class , is the supremum…
Avoiding squares over words with lists of size three amongst four symbols
Matthieu Rosenfeld
In 2007, Grytczuk conjecture that for any sequence of alphabets of size there exists a square-free infinite word such that for all , the -th letter…
Avoiding Square-Free Words on Free Groups
Golnaz Badkobeh, Tero Harju, Pascal Ochem +1
We consider sets of factors that can be avoided in square-free words on two-generator free groups. The elements of the group are presented in terms of 0,1,2,3 such that 0 and 2 (re…
Nonrepetitively 3-colorable subdivisions of graphs with a logarithmic number of subdivisions per edge
Matthieu Rosenfeld
We show that for every graph and every graph obtained by subdividing each edge of at least , is nonrepetitively 3-colorable. In fact, we show that $…
Another approach to non-repetitive colorings of graphs of bounded degree
Matthieu Rosenfeld
We propose a new proof technique that aims to be applied to the same problems as the Lovász Local Lemma or the entropy-compression method. We present this approach in the context o…
Nice formulas, -formulas, and palindrome patterns
Pascal Ochem, Matthieu Rosenfeld
We characterize the formulas that are avoided by every -free word for some . We study the avoidability index of formulas whose fragments are of the form . The largest…
Bounding the number of -dominating sets in trees, forests and graphs of bounded pathwidth
Matthieu Rosenfeld
The notion of -dominating set generalizes many notions including dominating set, induced matching, perfect codes or independent sets. Bounds on the maximal number of such (m…
Avoiding two consecutive blocks of same size and same sum over
Michaël Rao, Matthieu Rosenfeld
A long standing question asks whether is uniformly 2-repetitive [Justin 1972, Pirillo and Varricchio, 1994], that is, whether there is an infinite sequence over a fini…