Improved bounds on acyclic edge colouring
نویسندگان
چکیده
We prove that, the acyclic chromatic index a′(G) ≤ 6∆ for all graphs with girth at least 9. We extend the same method to obtain a bound of 4.52∆ with the girth requirement g ≥ 220. We also obtain a relationship between g and a′(G).
منابع مشابه
Acyclic Edge Colouring of Partial 2-Trees
An acyclic edge colouring of a graph is a proper edge colouring 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 colouring using k colours and it is denoted by a′(G). Here, we obtain tight estimates on a′(G) for nontrivial subclasses of the family of 2-degenerate graphs. Specifically, we obtain values of...
متن کاملSome graph classes satisfying acyclic edge colouring conjecture
We present some classes of graphs which satisfy the acyclic edge colouring conjecture which states that any graph can be acyclically edge coloured with at most ∆ + 2 colours.
متن کاملAcyclic 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 کاملAcyclic edge colouring of plane 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 کاملImproved Upper Bounds on $a'(G\Box H)$
The acyclic edge colouring problem is extensively studied in graph theory. The corner-stone of this field is a conjecture of Alon et. al.[1] that a′(G) ≤ ∆(G) + 2. In that and subsequent work, a′(G) is typically bounded in terms of ∆(G). Motivated by this we introduce a term gap(G) defined as gap(G) = a′(G) − ∆(G). Alon’s conjecture can be rephrased as gap(G) ≤ 2 for all graphs G. In [5] it was...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 19 شماره
صفحات -
تاریخ انتشار 2005