The circular chromatic index of Goldberg snarks
نویسنده
چکیده
We determine the exact values of the circular chromatic index of the Goldberg snarks, and of a related family, the twisted Goldberg snarks.
منابع مشابه
Circular Chromatic Index of Generalized Blanusa Snarks
In his Master’s thesis, Ján Mazák proved that the circular chromatic index of the type 1 generalized Blanuša snark B n equals 3+ 2 n . This result provided the first infinite set of values of the circular chromatic index of snarks. In this paper we show the type 2 generalized Blanuša snark B n has circular chromatic index 3 + 1 b1+3n/2c . In particular, this proves that all numbers 3 + 1/n with...
متن کاملThe Circular Chromatic Index of Flower Snarks
We determine the circular chromatic index of flower snarks, by showing that χc(F3) = 7/2, χ ′ c(F5) = 17/5 and χ ′ c(Fk) = 10/3 for every odd integer k ≥ 7, where Fk denotes the flower snark on 4k vertices.
متن کاملAsymptotic Lower Bounds on Circular Chromatic Index of Snarks
We prove that the circular chromatic index of a cubic graph G with 2k vertices and chromatic index 4 is at least 3 + 2/k. This bound is (asymptotically) optimal for an infinite class of cubic graphs containing bridges. We also show that the constant 2 in the above bound can be increased for graphs with larger girth or higher connectivity. In particular, if G has girth at least 5, its circular c...
متن کاملThe hunting of a snark with total chromatic number 5
A snark is a cyclically-4-edge-connected cubic graph with chromatic index 4. In 1880, Tait proved that the Four-Color Conjecture is equivalent to the statement that every planar bridgeless cubic graph has chromatic index 3. The search for counter-examples to the FourColor Conjecture motivated the definition of the snarks. A k-total-coloring of G is an assignment of k colors to the edges and ver...
متن کاملThe total-chromatic number of some families of snarks
The total chromatic number χ T (G) is the least number of colours needed to colour the vertices and edges of a graph G, such that no incident or adjacent elements (vertices or edges) receive the same colour. It is known that the problem of determining the total chromatic number is NP-hard and it remains NP-hard even for cubic bipartite graphs. Snarks are simple connected bridgeless cubic graphs...
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:
- Discrete Mathematics
دوره 307 شماره
صفحات -
تاریخ انتشار 2007