The Circular Chromatic Index of Flower Snarks
نویسندگان
چکیده
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.
منابع مشابه
The circular chromatic index of Goldberg snarks
We determine the exact values of the circular chromatic index of the Goldberg snarks, and of a related family, the twisted Goldberg snarks.
متن کاملCircular 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 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 کاملDiana Sasaki Simone Dantas Celina
Snarks are cubic bridgeless graphs of chromatic index 4 which had their origin in the search of counterexamples to the Four Color Conjecture. In 2003, Cavicchioli et al. proved that for snarks with less than 30 vertices, the total chromatic number is 4, and proposed the problem of finding (if any) the smallest snark which is not 4-total colorable. Several families of snarks have had their total...
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
عنوان ژورنال:
- Electr. J. Comb.
دوره 13 شماره
صفحات -
تاریخ انتشار 2006