Degree-bounded vertex partitions

نویسندگان

  • Benjamin McClosky
  • Illya V. Hicks
چکیده

This paper studies degree-bounded vertex partitions, considers analogues for wellknown results on the chromatic number and graph perfection, and presents two algorithms for constructing degree-bounded vertex partitions. The first algorithm minimizes the number of partition classes. The second algorithm minimizes a weighted sum of the partition classes where the weight of a partition class depends on the level of adjacency among its vertices.

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

Partitioning into Two Graphs with Only Small Components

The paper presents several results on edge partitions and vertex partitions of graphs into graphs with bounded size components. We show that every graph of bounded tree-width and bounded maximum degree admits such partitions. We also show that an arbitrary graph of maximum degree three has a vertex partition into two graphs, each of which has components on at most two vertices, and an edge part...

متن کامل

Partitioning into graphs with only small components

The paper presents several results on edge partitions and vertex partitions of graphs into graphs with bounded size components. We show that every graph of bounded tree-width and bounded maximum degree admits such partitions. We also show that an arbitrary graph of maximum degree four has a vertex partition into two graphs, each of which has components on at most 57 vertices. Some generalizatio...

متن کامل

k-forested choosability of graphs with bounded maximum average degree

A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...

متن کامل

On the extremal total irregularity index of n-vertex trees with fixed maximum degree

In the extension of irregularity indices, Abdo et. al. [1] defined the total irregu-larity of a graph G = (V, E) as irrt(G) = 21 Pu,v∈V (G) du − dv, where du denotesthe vertex degree of a vertex u ∈ V (G). In this paper, we investigate the totalirregularity of trees with bounded maximal degree Δ and state integer linear pro-gramming problem which gives standard information about extremal trees a...

متن کامل

Co-2-plex vertex partitions

This paper studies co-k-plex vertex partitions and more specifically co-2-plex vertex partitions. Co-k-plexes and k-plexes were first introduced in 1978 in the context of social network analysis. However, the study of co-k-plex vertex partitions, or the decomposition of graphs into degree bounded subgraphs, dates back at least to the work of Lovasz in 1966. In this paper, we derive analogues fo...

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 2008