Acyclic edge coloring of triangle-free 1-planar graphs
نویسندگان
چکیده
منابع مشابه
Acyclic Edge Coloring of Triangle Free Planar Graphs
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(G). It was conjectured by Alon, Sudakov and Zaks (and much earlier by Fiamcik) that a(G) ≤ ∆ + 2, where ∆ = ∆(G) denotes the maximum degree of the gra...
متن کاملEdge Coloring of Triangle-Free 1-Planar Graphs
it is shown that each triangle-free 1-planar graph with maximum degree $\Delta\geq7$ can be $\Delta$-colorable by Discharging Method.
متن کاملAcyclic Edge coloring of Planar Graphs
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(G). It was conjectured by Alon, Sudakov and Zaks (and much earlier by Fiamcik) that a(G) ≤ ∆ + 2, where ∆ = ∆(G) denotes the maximum degree of the gra...
متن کاملFractional Coloring of Triangle-Free Planar Graphs
We prove that every planar triangle-free graph on n vertices has fractional chromatic number at most 3− 1 n+1/3 .
متن کاملAcyclic chromatic index of triangle-free 1-planar graphs
An acyclic edge coloring of a graph G is a proper edge coloring such that every cycle is colored with at least three colors. The acyclic chromatic index χa(G) of a graph G is the least number of colors in an acyclic edge coloring of G. It was conjectured that χa(G) ≤ ∆(G) + 2 for any simple graph G with maximum degree ∆(G). A graph is 1-planar if it can be drawn on the plane such that every edg...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Mathematica Sinica, English Series
سال: 2015
ISSN: 1439-8516,1439-7617
DOI: 10.1007/s10114-015-4479-y