Grundy number on P4-classes
نویسندگان
چکیده
In this article, we define a new class of graphs, the fat-extended P4-laden graphs, and we show a polynomial time algorithm to determine the Grundy number of the graphs in this class. This result implies that the Grundy number can be found in polynomial time for any graph of the following classes: P4-reducible, extended P4-reducible, P4-sparse, extended P4-sparse, P4-extendible, P4-lite, P4-tidy, P4-laden and extended P4-laden, which are all strictly contained in the fat-extended P4laden class.
منابع مشابه
The result for the grundy number on p4 classes
Our work becomes integrated into the general problem of the stability of the network ad hoc. Some, works attacked (affected) this problem. Among these works, we find the modelling of the network ad hoc in the form of a graph. We can resume the problem of coherence of the network ad hoc of a problem of allocation of frequency We study a new class of graphs, the fat-extended P4 graphs, and we giv...
متن کاملRestricted coloring problems
In this paper, we obtain polynomial time algorithms to determine the acyclic chromatic number, the star chromatic number and the harmonious chromatic number of P4-tidy graphs and (q, q − 4)-graphs, for every fixed q. These classes include cographs, P4-sparse and P4-lite graphs. We also obtain a polynomial time algorithm to determine the Grundy number of (q, q − 4)-graphs. All these coloring pro...
متن کاملOn the Grundy number of graphs with few P4's
The Grundy number of a graph G is the largest number of colors used by any execution of the greedy algorithm to color G. The problem of determining the Grundy number of G is polynomial if G is a P 4-free graph and N P-hard if G is a P 5-free graph. In this article, we define a new class of graphs, the fat-extended P 4-laden graphs, and we show a polynomial time algorithm to determine the Grundy...
متن کاملMaximization coloring problems on graphs with few P4
Given a graph G= (V,E), a greedy coloring of G is a proper coloring such that, for each two colors i< j, every vertex of V (G) colored j has a neighbor with color i. The greatest k such that G has a greedy coloring with k colors is the Grundy number of G. A b-coloring of G is a proper coloring such that every color class contains a vertex which is adjacent to at least one vertex in every other ...
متن کاملA linear algorithm for the grundy number of a tree
A coloring of a graph G = (V ,E) is a partition {V1, V2, . . . , Vk} of V into independent sets or color classes. A vertex v ∈ Vi is a Grundy vertex if it is adjacent to at least one vertex in each color class Vj for every j <i. A coloring is a Grundy coloring if every color class contains at least one Grundy vertex, and the Grundy number of a graph is the maximum number of colors in a Grundy c...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 35 شماره
صفحات -
تاریخ انتشار 2009