Entropy Compression Method and Legitimate Colorings in Projective Planes

We prove that the entropy compression method systematized by L. Esperet and A. Parreau [11] can be applied to any problem formulated in the variable version of the Lov\'asz Local Lemma. As an application, we prove the existence of legitimate colorings for projective planes with small orders, which extends results of N. Alon and Z. F\"uredi [2]. In fact, we allow different numbers of colors, proving that projective planes of any order can be legitimate colored with 42 colors.Comment: 8 pages, 1 figur

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

We establish a connection between the entropy compression method and the Moser-Tardos algorithmic version of the Lov\'asz local lemma through the cluster expansion of the subset gas. We also show that the Moser-Tardos resampling algorithm and the entropy compression bactracking algorithm produce identical bounds

Compress\~ao de Entropia e Colora\c{c}\~oes Leg\'itimas em Planos Projetivos

We prove that the entropy compression method systematized by L. Esperet and A. Parreau can be applied to any problem formulated in the variable version of the Lovasz Local Lemma. As an application, we prove the existence of legitimate colorings for projective planes with small orders, which extends results of N. Alon and Z. Fured. In fact, we allow different numbers of colors, proving that projective planes of any order can be legitimate colored with 42 colors.Comment: in Portugues