Interval Edge Colorings of Mobius Ladders

نویسنده

  • Petros A. Petrosyan
چکیده

An interval edge t-coloring of a graph G is a proper edge coloring of G with colors 1,2...,t such that at least one edge of G is colored by color i,i=1,2...,t, and the edges incident with each vertex x are colored by d_{G}(x) consecutive colors, where d_{G}(x) is the degree of the vertex x in G. For Mobius ladders the existence of this coloring is proved and all possible numbers of colors in such colorings are found.

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

On Interval Edge Colorings of Biregular Bipartite Graphs With Small Vertex Degrees

A proper edge coloring of a graph with colors 1, 2, 3, . . . is called an interval coloring if the colors on the edges incident to each vertex form an interval of integers. A bipartite graph is (a, b)-biregular if every vertex in one part has degree a and every vertex in the other part has degree b. It has been conjectured that all such graphs have interval colorings. We prove that all (3, 6)-b...

متن کامل

Interval cyclic edge-colorings of graphs

A proper edge-coloring of a graph G with colors 1, , t  is called an interval cyclic t  coloring if all colors are used, and the edges incident to each vertex ( ) v V G  are colored with ( ) G d v consecutive colors by modulo t , where ( ) G d v is the degree of the vertex v in G . In this paper some properties of interval cyclic edge-colorings are investigated. Also, we give some bounds for...

متن کامل

Interval edge-colorings of graph products

An interval t coloring of a graph is a proper edgecoloring of with colors 1, such that at least one edge of G is colored by and the edges incident to each vertex − G G 2, , t ... , 1, 2, , , i i t = ... ( ) v V G ∈ are colored by consecutive colors, where is the degree of the vertex in . In this paper interval edge-colorings of various graph products are investigated. ( ) G d v ( ) G d v v G

متن کامل

Lower bounds for the greatest possible number of colors in interval edge colorings of bipartite cylinders and bipartite tori

An interval edge t − coloring of a graph G is a proper edge coloring of G with colors 1, 2, , t ... such that at least one edge of G is colored by color , 1, 2, , i i t = ... , and the edges incident with each vertex ( ) v V G ∈ are colored by ( ) G d v consecutive colors, where ( ) G d v is the degree of the vertex v in G . In this paper interval edge colorings of bipartite cylinders and bipar...

متن کامل

Estimates for the number of vertices with an interval spectrum in proper edge colorings of some graphs

For an undirected, simple, finite, connected graph G, we denote by V (G) and E(G) the sets of its vertices and edges, respectively. A function φ : E(G) → {1, 2, . . . , t} is called a proper edge t-coloring of a graph G if all colors are used and no two adjacent edges receive the same color. An arbitrary nonempty subset of consecutive integers is called an interval. The set of all proper edge t...

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:
  • CoRR

دوره abs/0801.0159  شماره 

صفحات  -

تاریخ انتشار 2007