List Edge-Colorings of Series-Parallel Graphs

List Edge-Colorings of Series-Parallel Graphs

It is proved that for every integer k for every simple series parallel graph G with maximum degree at most k and for every collection L e e E G of sets each of size at least k there exists a proper edge coloring of G such that for every edge e E G the color of e belongs to L e

List Total Colorings of Series-Parallel Graphs

A total coloring of a graph G is a coloring of all elements of G, i.e., vertices and edges, in such a way that no two adjacent or incident elements receive the same color. Let L(x) be a set of colors assigned to each element x of G. Then a list total coloring of G is a total coloring such that each element x receives a color contained in L(x). The list total coloring problem asks whether G has ...

On list edge-colorings of subcubic graphs

In this paper we study list edge-colorings of graphs with small maximal degree. In particular, we show that simple subcubic graphs are '10/3-edge choosable'. The precise meaning of this statement is that no matter how we prescribe arbitrary lists of three colors on edges of a subgraph H of G such that A(H)~< 2, and prescribe lists of four colors on E(G)\E(H), the subcubic graph G will have an e...

List Edge Colorings of Outerplanar Graphs

Sufficient Condition and Algorithm for List Total Colorings of Series-Parallel Graphs

A total coloring of a graph G is a coloring of all elements of G, i.e. vertices and edges, such that no two adjacent or incident elements receive the same color. Let L(x) be a set of colors assigned to each element x of G. Then a list total coloring of G is a total coloring such that each element x receives a color contained in L(x). The list total coloring problem asks whether G has a list tot...