On the set of circular total chromatic numbers of graphs
نویسنده
چکیده
For every integer r > 3 and every ε > 0 we construct a graph with maximum degree r − 1 whose circular total chromatic number is in the interval (r, r + ε). This proves that (i) every integer r > 3 is an accumulation point of the set of circular total chromatic numbers of graphs, and (ii) for every ∆ > 2, the set of circular total chromatic numbers of graphs with maximum degree ∆ is infinite. All these results hold for the set of circular total chromatic numbers of bipartite graphs as well.
منابع مشابه
Incidence dominating numbers of graphs
In this paper, the concept of incidence domination number of graphs is introduced and the incidence dominating set and the incidence domination number of some particular graphs such as paths, cycles, wheels, complete graphs and stars are studied.
متن کاملCircular Chromatic Numbers and Fractional Chromatic Numbers of Distance Graphs with Distance Sets Missing An Interval
Suppose S is a subset of a metric spaceM with a metric δ, and D a subset of positive real numbers. The distance graph G(S, D), with a distance set D, is the graph with vertex set S in which two vertices x and y are adjacent iff δ(x, y) ∈ D. Distance graphs, first studied by Eggleton et al. [7], were motivated by the well-known plane-coloring problem: What is the minimum number of colors needed ...
متن کاملCircular Chromatic Numbers of Distance Graphs with Distance Sets Missing Multiples
Given a set D of positive integers, the distance graph G(Z , D) has all integers as vertices, and two vertices are adjacent if and only if their difference is in D; that is, the vertex set is Z and the edge set is {uv : |u − v| ∈ D}. We call D the distance set. This paper studies chromatic and circular chromatic numbers of some distance graphs with certain distance sets. The circular chromatic ...
متن کاملJust chromatic exellence in fuzzy graphs
A fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. The concept of fuzzy sets and fuzzy relations was introduced by L.A.Zadeh in 1965cite{zl} and further studiedcite{ka}. It was Rosenfeldcite{ra} who considered fuzzy relations on fuzzy sets and developed the theory of fuzzy graphs in 1975. The concepts of fuzzy trees, blocks, bridges and cut nodes in fuzzy graph has been studi...
متن کاملDistance Graphs and T-Coloring
We discuss relationships among T-colorings of graphs and chromatic numbers, fractional chromatic numbers, and circular chromatic numbers of distance graphs. We first prove that for any finite integral set T that contains 0, the asymptotic T-coloring ratio R(T ) is equal to the fractional chromatic number of the distance graph G(Z, D), where D=T&[0]. This fact is then used to study the distance ...
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 313 شماره
صفحات -
تاریخ انتشار 2013