On Coloring Squares of Outerplanar Graphs
نویسندگان
چکیده
We study vertex colorings of the square G of an outerplanar graph G. We find the optimal bound of the inductiveness, chromatic number and the clique number of G as a function of the maximum degree ∆ of G for all ∆ ∈ N. As a bonus, we obtain the optimal bound of the choosability (or the list-chromatic number) of G when ∆ ≥ 7. In the case of chordal outerplanar graphs, we classify exactly which graphs have parameters exceeding the absolute minimum. 2000 MSC: 05C05, 05C12, 05C15.
منابع مشابه
On Group Choosability of Total Graphs
In this paper, we study the group and list group colorings of total graphs and present group coloring versions of the total and list total colorings conjectures.We establish the group coloring version of the total coloring conjecture for the following classes of graphs: graphs with small maximum degree, two-degenerate graphs, planner graphs with maximum degree at least 11, planner graphs withou...
متن کاملAdvice Complexity of the Online Vertex Coloring Problem
We study online algorithms with advice for the problem of coloring graphs which come as input vertex by vertex. We consider the class of all 3-colorable graphs and its sub-classes of chordal and maximal outerplanar graphs, respectively. We show that, in the case of the first two classes, for coloring optimally, essentially log2 3 advice bits per vertex (bpv) are necessary and sufficient. In the...
متن کاملOn list-coloring extendable outerplanar graphs∗
We investigate a variation on Thomassen’s 2and 3-extendability of precoloring extensions for list-coloring graphs. For an outerplanar graph G with i, j ≤ 2, we say that G is {i, j}-extendable if for every pair of nonadjacent vertices x and y, whenever x is assigned an i-list, y is assigned a j-list, and all other vertices have a 3-list, G is list-colorable. We characterize the {1, 1}and the {1,...
متن کاملTotal coloring of pseudo-outerplanar graphs
A graph is pseudo-outerplanar if each of its blocks has an embedding in the plane so that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. In this paper, the total coloring conjecture is completely confirmed for pseudoouterplanar graphs. In particular, it is proved that the total chromatic number of every pseudo-...
متن کاملOriented coloring of triangle-free planar graphs and 2-outerplanar graphs
A graph is planar if it can be embedded on the plane without edge-crossing. A graph is 2-outerplanar if it has a planar embedding such that the subgraph obtained by removing the vertices of the external face is outerplanar (i.e. with all its vertices on the external face). An oriented k-coloring of an oriented graph G is a homomorphism from G to an oriented graph H of order k. We prove that eve...
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:
دوره شماره
صفحات -
تاریخ انتشار 2004