List Edge Coloring of Outer-1-planar Graphs

Adapted list coloring of planar graphs

Given a (possibly improper) edge-colouring F of a graph G, a vertex colouring of G is adapted to F if no colour appears at the same time on an edge and on its two endpoints. If for some integer k, a graph G is such that given any list assignment L to the vertices of G, with |L(v)| ≥ k for all v, and any edgecolouring F of G, G admits a colouring c adapted to F where c(v) ∈ L(v) for all v, then ...

Acyclic list 7-coloring of planar graphs

Theacyclic list chromatic numberof every planar graph is proved to be at most 7. 2002 Wiley Periodicals, Inc. J Graph Theory 40: 83–90, 2002

List VEF Coloring of Planar Graphs

In this paper the new coloring of planar, VEF-coloring, will be introduced. A VEF coloring of a simple planar graph G is a proper coloring of all elements, including vertices, edges and faces of G. We will give two conjectures for the upper bound of VEF and VEF-list coloring of a simple planar graph. However, we will prove these conjectures for planar graphs with a maximum degree of at least 12...

Acyclic List Edge Coloring of Graphs

Dynamic coloring and list dynamic coloring of planar graphs

A dynamic chromatic number χd(G) of a graph G is the least number k such that G has a proper k-coloring of the vertex set V (G) so that for each vertex of degree at least 2, its neighbors receive at least two distinct colors. We show that χd(G) ≤ 4 for every planar graph except C5, which was conjectured in [5]. The list dynamic chromatic number chd(G) of G is the least number k such that for an...