Generalised acyclic edge colourings of graphs with large girth

نویسندگان

Stefanie Gerke

Melanie Raemy

چکیده

An edge colouring of a graph G is called acyclic if it is proper and every cycle contains at least three colours. We show that for every ε > 0, there exists a g = g(ε) such that if G has girth at least g then G admits an acyclic edge colouring with at most (1 + ε)∆ colours.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Acyclic Coloring of Graphs

In this report we obtain (good) upper bounds on the acyclic chromatic index of graphs obtained as the tensor product of two (or more) graphs, in terms of the acyclic chromatic indices of those factor graphs in the tensor product. Our results assume that optimal colourings for the factor graphs are given and our algorithms extend these colourings to obtain good (close to optimal) colourings of t...

متن کامل

A note on n-tuple colourings and circular colourings of planar graphs with large odd girth

International Journal of Computer Mathematics Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713455451 A note on n-tuple colourings and circular colourings of planar graphs with large odd girth P. šparl ab; J. žerovnik ac a IMFM, Slovenia b FG, University of Maribor, Slovenia c FS, University of Maribor, Slov...

متن کامل

Frugal Colouring of Graphs

A k-frugal colouring of a graph G is a proper colouring of the vertices of G such that no colour appears more than k times in the neighbourhood of a vertex. This type of colouring was introduced by Hind, Molloy and Reed in 1997. In this paper, we study the frugal chromatic number of planar graphs, planar graphs with large girth, and outerplanar graphs, and relate this parameter with several wel...

متن کامل

Acyclic edge-colouring of planar graphs∗

A proper edge-colouring with the property that every cycle contains edges of at least three distinct colours is called an acyclic edge-colouring. The acyclic chromatic index of a graph G, denoted χa(G), is the minimum k such that G admits an acyclic edge-colouring with k colours. We conjecture that if G is planar and ∆(G) is large enough then χa(G) = ∆(G). We settle this conjecture for planar g...

متن کامل