Acyclic Colorings and Triangulations of Weakly Chordal Graphs
نویسنده
چکیده
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 linear time algorithms for a number of graph classes contained within this class, such as permutation graphs and distance-hereditary graphs.
منابع مشابه
Bounding cochordal cover number of graphs via vertex stretching
It is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (Castelnuovo-Mumford) regularity. As a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph G are equal provided G is well-covered bipa...
متن کاملComplement of Special Chordal Graphs and Vertex Decomposability
In this paper, we introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially Cohen-Macaulay.
متن کاملNegative 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 کاملAcyclic 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 کاملMeasurable 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