Defective circular coloring

نویسنده

William Klostermeyer

چکیده

The concept of a defective circular coloring is introduced, and results shown for planar, series-parallel, and outerplanar graphs. Numerous problems are also stated.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Fractional, Circular, and Defective Coloring of Series-Parallel Graphs

In this note we consider colorings of series-parallel graphs. Specifically, we provide bounds on their fractional and circular chromatic numbers and the defective version of these parameters. The main result is that the fractional chromatic number of any series-parallel graph of odd girth k is exactly 2k/(k − 1).

متن کامل

Fractional and circular 1-defective colorings of outerplanar graphs

A graph is called fractional ( r s , d ) -defective colorable if its vertices can be colored with r colors in such a way that each vertex receives s distinct colors and has at most d defects (a defect corresponds to the situation when two adjacent vertices are assigned with non-disjoint sets). We show that each outerplanar graph having no triangle faces sharing a vertex is fractional ( 7 3 , 1 ...

متن کامل

Defective List Colorings of Planar Graphs

We combine the concepts of list colorings of graphs with the concept of defective colorings of graphs and introduce the concept of defective list colorings. We apply these concepts to vertex colorings of various classes of planar graphs. A defective coloring with defect d is a coloring of the vertices such that each color class corresponds to an induced subgraph with maximum degree at most d. A...

متن کامل

Bounds and Fixed-Parameter Algorithms for Weighted Improper Coloring

We study the weighted improper coloring problem, a generalization of defective coloring. We present some hardness results and in particular we show that weighted improper coloring is not fixed-parameter tractable when parameterized by pathwidth. We generalize bounds for defective coloring to weighted improper coloring and give a bound for weighted improper coloring in terms of the sum of edge w...

متن کامل