Combinatorica
Further algorithmic aspects of the local lemma
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Bounds on the Complex Zeros of (Di)Chromatic Polynomials and Potts-Model Partition Functions
Combinatorics, Probability and Computing
Regions without complex zeros for chromatic polynomials on graphs with bounded degree
Combinatorics, Probability and Computing
Acyclic edge colorings of graphs
Journal of Graph Theory
Journal of Graph Theory
Acyclic Edge Colouring of Outerplanar Graphs
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Acyclic edge coloring of graphs with maximum degree 4
Journal of Graph Theory
A constructive proof of the general lovász local lemma
Journal of the ACM (JACM)
Random Structures & Algorithms
An improvement of the lovász local lemma via cluster expansion
Combinatorics, Probability and Computing
The acyclic edge coloring of planar graphs without a 3-cycle adjacent to a 4-cycle
Discrete Applied Mathematics
Acyclic edge coloring of graphs
Discrete Applied Mathematics
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Given a graph G with maximum degree @D=3, we prove that the acyclic edge chromatic number a^'(G) of G is such that a^'(G)@?@?9.62(@D-1)@?. Moreover we prove that: a^'(G)@?@?6.42(@D-1)@? if G has girth g=5; a^'(G)@?@?5.77(@D-1)@? if G has girth g=7; a^'(G)@?@?4.52(@D-1)@? if g=53; a^'(G)@?@D+2 if g=@?25.84@Dlog@D(1+4.1/log@D)@?. We further prove that the acyclic (vertex) chromatic number a(G) of G is such that a(G)@?@?6.59@D^4^/^3+3.3@D@?. We also prove that the star-chromatic number @g"s(G) of G is such that @g"s(G)@?@?4.34@D^3^/^2+1.5@D@?. We finally prove that the @b-frugal chromatic number @g^@b(G) of G is such that @g^@b(G)@?@?max{k"1(@b)@D,k"2(@b)@D^1^+^1^/^@b/(@b!)^1^/^@b}@?, where k"1(@b) and k"2(@b) are decreasing functions of @b such that k"1(@b)@?[4,6] and k"2(@b)@?[2,5]. To obtain these results we use an improved version of the Lovasz Local Lemma due to Bissacot et al. (2011) [6].