Acyclic Edge Coloring of Chordal Graphs with Bounded Degree

An acyclic edge coloring of a graph G is a proper edge coloring such that 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, we confirm the conjecture for chordal graphs G with $$\Delta \le 6$$ Δ ≤ 6 .

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

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

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

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

[5]  Noga Alon,et al.  Acyclic edge colorings of graphs , 2001, J. Graph Theory.

[6]  Manu Basavaraju,et al.  Acyclic edge coloring of graphs with maximum degree 4 , 2009, J. Graph Theory.

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

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

[9]  Tao Wang,et al.  Further result on acyclic chromatic index of planar graphs , 2014, Discret. Appl. Math..

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

[11]  Pinar Heggernes,et al.  Enumerating minimal dominating sets in chordal graphs , 2016, Inf. Process. Lett..

[12]  Qiaojun Shu,et al.  Acyclic Edge Coloring of 4-Regular Graphs (II) , 2019 .

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

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

[15]  San Skulrattanakulchai,et al.  Acyclic colorings of subcubic graphs , 2004, Inf. Process. Lett..

[16]  Dimitrios M. Thilikos,et al.  Acyclic edge coloring through the Lovász Local Lemma , 2014, Theor. Comput. Sci..

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

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