Entropy Compression Method and Legitimate Colorings in Projective Planes

Abstract

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 Lovász 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. Füredi [2]. In fact, we allow different numbers of colors, proving that projective planes of any order can be legitimate colored with 42 colors.

8 pages, 1 figure

References in corpus (4)

• Acyclic edge-coloring using entropy compression
• Entropy compression method applied to graph colorings
• The Local Cut Lemma
• A local lemma via entropy compression

Cited by in corpus (1)

• A general framework for hypergraph colouring