منابع مشابه
Circular Chromatic Ramsey Number
Let χc(H) denote the circular chromatic number of a graph H. For graphs F and G, the circular chromatic Ramsey number Rχc(F,G) is the infimum of χc(H) over graphs H such that every red/blue edge-coloring of H contains a red copy of F or a blue copy of G. We characterize Rχc(F,G) in terms of a Ramsey problem for the families of homomorphic images of F and G. Letting zk = 3 − 2 −k, we prove that ...
متن کاملCircular chromatic number: a survey
The circular chromatic number chi (c)(G) of a graph G (also known as 'the star-chromatic number'), is a natural generalization of the chromatic number of a graph. In this paper, we survey results on this topic, concentrating on the relations among the circular chromatic number, the chromatic number and some other parameters of a graph. Some of the results and or proofs presented here are new. T...
متن کاملCircular Chromatic Number of Hypergraphs
The concept of circular chromatic number of graphs was introduced by Vince(1988). In this paper we define circular chromatic number of uniform hypergraphs and study their basic properties. We study the relationship between circular chromatic number with chromatic number and fractional chromatic number of uniform hypergraphs.
متن کاملThe chromatic Ramsey number of odd wheels
We prove that the chromatic Ramsey number of every odd wheel W2k+1, k ≥ 2 is 14. That is, for every odd wheel W2k+1, there exists a 14-chromatic graph F such that when the edges of F are two-coloured, there is a monochromatic copy of W2k+1 in F , and no graph F with chromatic number 13 has the same property. We ask whether a natural extension of odd wheels to the family of generalized Mycielski...
متن کاملLarge Chromatic Number and Ramsey Graphs
Let Q(n, χ) denote the minimum clique size an n-vertex graph can have if its chromatic number is χ . Using Ramsey graphs we give an exact, albeit implicit, formula for the case χ ≥ (n + 3)/2.
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2017
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2017.v8.n1.a7