Circular Chromatic Number and Graph Minors
نویسنده
چکیده
This paper proves that for any integer n ≥ 4 and any rational number r, 2 ≤ r ≤ n − 2, there exists a graph G which has circular chromatic number r and which does not contain Kn as a minor.
منابع مشابه
The distinguishing chromatic number of bipartite graphs of girth at least six
The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. The distinguishing chromatic number $chi_{D}(G)$ of $G$ is defined similarly, where, in addition, $f$ is assumed to be a proper labeling. We prove that if $G$ is a bipartite graph of girth at least six with the maximum ...
متن کاملA note on the circular chromatic number of circular perfect planar graphs
Computing the circular chromatic number of a given planar graph is NP-complete, as it is already NP-complete to compute its chromatic number. In this note, we prove that the circular clique number of a planar graph, and therefore the circular chromatic number of a circular perfect graph, is computable in O(ne) time; outerplanar graphs are circular perfect.
متن کاملComputing Multiplicative Zagreb Indices with Respect to Chromatic and Clique Numbers
The chromatic number of a graph G, denoted by χ(G), is the minimum number of colors such that G can be colored with these colors in such a way that no two adjacent vertices have the same color. A clique in a graph is a set of mutually adjacent vertices. The maximum size of a clique in a graph G is called the clique number of G. The Turán graph Tn(k) is a complete k-partite graph whose partition...
متن کاملThe circular chromatic number of series-parallel graphs of large odd girth
In this paper, we consider the circular chromatic number c (G) of series-parallel graphs G. It is well known that series-parallel graphs have chromatic number at most 3. Hence their circular chromatic number is also at most 3. If a series-parallel graph G contains a triangle , then both the chromatic number and the circular chromatic number of G are indeed equal to 3. We shall show that if a se...
متن کاملList-chromatic Number and the Chromatic Number in Minor-closed and Odd-minor-closed Classes of Graphs
It is well-known (Feige and Kilian [24], H̊astad [39]) that approximating the chromatic number within a factor of n1−ε cannot be done in polynomial time for ε > 0, unless coRP = NP. Computing the list-chromatic number is much harder than determining the chromatic number. It is known that the problem of deciding if the list-chromatic number is k, where k ≥ 3, is Πp2-complete [37]. In this paper, ...
متن کامل