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 کاملCircular Chromatic Number and Mycielski Graphs
As a natural generalization of graph coloring, Vince introduced the star chromatic number of a graph G and denoted it by χ∗(G). Later, Zhu called it circular chromatic number and denoted it by χc(G). Let χ(G) be the chromatic number of G. In this paper, it is shown that if the complement of G is non-hamiltonian, then χc(G)=χ(G). Denote by M(G) the Mycielski graph of G. Recursively define Mm(G)=...
متن کاملThe circular chromatic number of a digraph
We introduce the circular chromatic number χc of a digraph and establish various basic results. They show that the coloring theory for digraphs is similar to the coloring theory for undirected graphs when independent sets of vertices are replaced by acyclic sets. Since the directed k-cycle has circular chromatic number k/(k − 1), for k ≥ 2, values of χc between 1 and 2 are possible. We show tha...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2001
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00217-x