Improved upper bound for the degenerate and star chromatic numbers of graphs

Moser–Tardos resampling algorithm, entropy compression method and the subset gas

“…Esperet and Parreau suggested, through examples and applications, that their algorithm could be adapted to treat most of the applications in graph coloring problems covered by the LLL. Indeed, this was confirmed in several successive papers [8,14,15,25,27,40,43,44,46], where the Esperet-Parreau scheme was applied to various graph coloring problems and beyond, generally improving previous results obtained via the LLL/CELL (sometimes the improvement is more noticeable, sometimes less). However, in all papers mentioned above, the Esperet-Parreau algorithmic scheme, usually called entropy compression method (the name is probably due to Tao [49]), has been commonly utilized as a set of ad hoc instructions to be implemented on a case-by-case basis.…”

Moser-Tardos resampling algorithm, entropy compression method and the subset gas

“…Esperet and Parreau suggested, through further examples and applications, that their algorithm could be adapted to treat most of the applications in graph coloring problems covered by the LLL. Indeed, this was confirmed in several successive papers [26,42,39,43,15,14,45,24,8], where the Esperet-Parreau scheme has been applied to various graph coloring problems and beyond, generally improving previous results obtained via the LLL/CELL (sometimes the improvement is more sensible, sometimes less). However, in all papers mentioned above the Esperet-Parreau algorithmic scheme, usually called entropy compression method (the name is probably due to Tao [48]), has been commonly utilized as a set of ad hoc instructions to be implemented on a case-by-case basis.…”

Entropy Compression Method and Legitimate Colorings in Projective Planes

“…Also in 2013, Esperet and Parreau [11] systematized this approach for a certain group of problems. Many results were recently obtained applying this last method as in [8,9,11,13,20,21].…”