Acyclic Improper Colorings of Graphs

نویسندگان

  • P. Boiron
  • E. Sopena
چکیده

In this paper, we introduce the new notion of acyclic improper colorings of graphs. An improper coloring of a graph G is a mapping c from the set of vertices of G to a set of colors such that for every color i, the subgraph induced by the vertices with color i satisses some property depending on i. Such an improper coloring is acyclic if for every two distinct colors i and j, the subgraph induced by all the edges linking a i-colored vertex and a j-colored vertex is acyclic. We prove that every outerplanar graph can be acyclically 2-colored in such a way that every monochromatic subgraph has degree at most ve and that this result is best possible. For planar graphs, we prove some negative results and state some open problems.

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

Acyclic improper choosability of graphs

We consider improper colorings (sometimes called generalized, defective or relaxed colorings) in which every color class has a bounded degree. We propose a natural extension of improper colorings: acyclic improper choosability. We prove that subcubic graphs are acyclically (3,1)∗-choosable (i.e. they are acyclically 3-choosable with color classes of maximum degree one). Using a linear time algo...

متن کامل

Negative results on acyclic improper colorings

Raspaud and Sopena showed that the oriented chromatic number of a graph with acyclic chromatic number k is at most k2. We prove that this bound is tight for k ≥ 3. We also consider acyclic improper colorings on planar graphs and partial ktrees. Finally, we show that some improper and/or acyclic colorings are NP-complete on restricted subclasses of planar graphs, in particular acyclic 3-colorabi...

متن کامل

Acrylic improper colorings of graphs

In this paper, we introduce the new notion of acyclic improper colorings of graphs. An improper coloring of a graph is a vertex-coloring in which adjacent vertices are allowed to have the same color, but each color class V i satisses some condition depending on i. Such a coloring is acyclic if there are no alternating 2-colored cycles. We prove that every outerplanar graph can be acyclically 2-...

متن کامل

Acyclic Colorings and Triangulations of Weakly Chordal Graphs

An acyclic coloring of a graph is a proper vertex coloring without bichromatic cycles. We show that the acyclic colorings of any weakly chordal graph G correspond to the proper colorings of triangulations of G. As a consequence, we obtain polynomial-time algorithms for the acyclic coloring problem and the perfect phylogeny problem on the class of weakly chordal graphs. Our results also imply li...

متن کامل

Measurable 3-colorings of Acyclic Graphs

This is the first of two lectures on measurable chromatic numbers given in June 2010 at the University of Barcelona. Our main result here is that acyclic locally finite analytic graphs on Polish spaces admit Baire measurable 3-colorings.

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1997