Acyclic Edge Coloring of 4-Regular Graphs (II)

A proper edge coloring is called acyclic if no bichromatic cycles are produced. It was conjectured that every simple graph G with maximum degree $$\Delta $$Δ is acyclically edge-$$(\Delta + 2)$$(Δ+2)-colorable. In this paper, combining some known results, we confirm the conjecture for graphs with $$\Delta =4$$Δ=4.

[1]  Bruce A. Reed,et al.  Acyclic Coloring of Graphs , 1991, Random Struct. Algorithms.

[2]  Manu Basavaraju,et al.  Acyclic edge coloring of 2-degenerate graphs , 2012, J. Graph Theory.

[3]  Manu Basavaraju,et al.  Acyclic edge coloring of graphs with maximum degree 4 , 2009 .

[4]  Qiaojun Shu,et al.  Acyclic Edge Coloring of 4-Regular Graphs Without 3-Cycles , 2019 .

[5]  Bruce A. Reed,et al.  Further algorithmic aspects of the local lemma , 1998, STOC '98.

[6]  Dimitrios M. Thilikos,et al.  On the Algorithmic Lovász Local Lemma and Acyclic Edge Coloring , 2015, ANALCO.

[7]  Manu Basavaraju,et al.  Acyclic Edge-Coloring of Planar Graphs , 2009, SIAM J. Discret. Math..

[8]  Manu Basavaraju,et al.  Acyclic edge coloring of subcubic graphs , 2008, Discret. Math..

[9]  Wei-Fan Wang,et al.  Acyclic chromatic indices of planar graphs with girth at least five , 2010, Journal of Combinatorial Optimization.

[10]  Edita Mácajová,et al.  Optimal acyclic edge-coloring of cubic graphs , 2012, J. Graph Theory.

[11]  Wei-Fan Wang,et al.  A new upper bound on the acyclic chromatic indices of planar graphs , 2012, Eur. J. Comb..

[12]  Noga Alon,et al.  Acyclic edge colorings of graphs , 2001 .

[13]  Aldo Procacci,et al.  Improved bounds on coloring of graphs , 2010, Eur. J. Comb..

[14]  Bin Liu,et al.  Acyclic edge chromatic number of outerplanar graphs , 2010 .

[15]  Aline Parreau,et al.  Acyclic edge-coloring using entropy compression , 2012, Eur. J. Comb..