Riste Škrekovski

A Theorem about the Channel Assignment Problem

A list channel assignment problem is a triple (G,L,w), where G is a graph, L is a function which assigns to each vertex of G a list of integers (colors), and w is a function which assigns to each edge of G a positive integer (its weight). A coloring c of the vertices of G is proper if c(v)\in L(v)

Coloring squares of planar graphs with girth six

for each vertex v and

List Improper Colourings of Planar Graphs

|c(u)-c(v)|\ge w(uv)

Total-Coloring of Plane Graphs with Maximum Degree Nine

for each edge uv. A weighted degree

List Total Colourings of Graphs

\deg_w(v)

Injective colorings of planar graphs with few colors

of a vertex v is the sum of the weights of the edges incident with v. If G is connected,

Graphs of degree 4 are 5-edge-choosable

|L(v)|>\deg_w(v)

Mathematical aspects of Wiener index

for at least one v, and

List-Coloring Squares of Sparse Subcubic Graphs

|L(v)|\ge\deg_w(v)

List improper colorings of planar graphs with prescribed girth

for all v, then a proper coloring always exists. A list channel assignment problem is balanced if