id: 06110313
dt: j
an: 06110313
au: Basavaraju, Manu; Chandran, L.Sunil
ti: Acyclic edge coloring of triangle-free planar graphs.
so: J. Graph Theory 71, No. 3-4, 365-385 (2012).
py: 2012
pu: John Wiley \& Sons, New York, NY
la: EN
cc: 
ut: acyclic edge coloring; acyclic edge chromatic number; planar graphs
ci: 
li: doi:10.1002/jgt.20651
ab: Summary: An acyclic edge coloring of a graph is a proper edge coloring such
    that there are no bichromatic cycles. The acyclic chromatic index of a
    graph is the minimum number $k$ such that there is an acyclic edge
    coloring using $k$ colors and is denoted by $a^{\prime}(G)$. It was
    conjectured by Alon, Sudakov and Zaks (and much earlier by Fiamcik)
    that $a^{\prime}(G) \le Δ+ 2$, where $Δ= Δ(G)$ denotes the maximum
    degree of the graph. If every induced subgraph $H$ of $G$satisfies the
    condition $|E(H)| \le 2|V(H)| - 1$, we say that the graph $G$ satisfies
    Property $A$. In this article, we prove that if $G$ satisfies Property
    $A$, then $a^{\prime}(G) \le Δ+ 3$. Triangle-free planar graphs
    satisfy Property $A$. We infer that $a^{\prime}(G) \le Δ+ 3$, if $G$
    is a triangle-free planar graph. Another class of graph which satisfies
    Property $A$ is 2-fold graphs (union of two forests).
rv: