Probing Graph Proper Total Colorings With Additional Constrained Conditions

نویسندگان

  • Bing Yao
  • Ming Yao
  • Xiangen Chen
چکیده

Graph colorings are becoming an increasingly useful family of mathematical models for a broad range of applications, such as time tabling and scheduling, frequency assignment, register allocation, computer security and so on. Graph proper total colorings with additional constrained conditions have been investigated intensively in the last decade year. In this article some new graph proper total colorings with additional constrained conditions are defined, and approximations to the chromatic numbers of these colorings are researched, as well as some graphs having these colorings have been verified. AMS Subject Classification (2000): 05C15

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

Perfect $2$-colorings of the Platonic graphs

In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and  the icosahedral graph.

متن کامل

D-strong Total Colorings of Graphs

If c : V ∪ E → {1, 2, . . . , k} is a proper total coloring of a graph G = (V,E) then the palette S[v] of a vertex v ∈ V is the set of colors of the incident edges and the color of v: S[v] = {c(e) : e = vw ∈ E} ∪ {c(v)}. A total coloring c distinguishes vertices u and v if S[u] 6= S[v]. A d-strong total coloring of G is a proper total coloring that distinguishes all pairs of vertices u and v wi...

متن کامل

Bounds on Edge Colorings with Restrictions on the Union of Color Classes

We consider constrained proper edge colorings of the following type: Given a positive integer j and a family F of connected graphs on 3 or more vertices, we require that the subgraph formed by the union of any j color classes has no copy of any member of F . This generalizes some well-known types of colorings such as acyclic edge colorings, distance-2 edge colorings, low treewidth edge coloring...

متن کامل

Extremal Colorings and Extremal Satisfiability

Combinatorial problems are often easy to state and hard to solve. A whole bunch of graph coloring problems falls into this class as well as the satisfiability problem. The classical coloring problems consider colorings of objects such that two objects which are in a relation receive different colors, e.g., proper vertex-colorings, proper edge-colorings, or proper face-colorings of plane graphs....

متن کامل

Nowhere-harmonic Colorings of Graphs

Abstract. Proper vertex colorings of a graph are related to its boundary map, also called its signed vertex-edge incidence matrix. The vertex Laplacian of a graph, a natural extension of the boundary map, leads us to introduce nowhere-harmonic colorings and analogues of the chromatic polynomial and Stanley’s theorem relating negative evaluations of the chromatic polynomial to acyclic orientatio...

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/1601.00883  شماره 

صفحات  -

تاریخ انتشار 2015