Equitable colorings of outerplanar graphs

List Edge Colorings of Outerplanar Graphs

On interval edge-colorings of outerplanar graphs

A proper edge-coloring of a graph G with colors 1, . . . , t is called an interval t-coloring if the colors of edges incident to any vertex of G form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. For an interval colorable graph G, the least value of t for which G has an interval t-coloring is denoted by w(G). A graph G is ...

Equitable Online-Colorings of Random Graphs

A proper graph coloring is called equitable if the sizes of every two color classes differ by at most one. We consider the following generalized notion of graph colorings: a vertex coloring of graph G is valid w.r.t. some fixed nonempty graph F if no color class induces a copy of F in G, i.e., there is no monochromatic copy of F in G. We propose and analyze an algorithm for computing valid equi...

Equitable Colorings of Bounded Treewidth Graphs

A proper coloring of a graph G is equitable if the sizes of any two color classes are differ by at most one. The related notion is `-bounded coloring where each of the color classes is of cardinality ≤ `. We consider the problems to determine for a given graph G (and a given integer `) whether G has an equitable (`-bounded) coloring. We prove that both problems can be solved in polynomial time ...

Equitable colorings of corona multiproducts of graphs

A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted χ=(G). It is known that this problem is NP-hard in general case and remains so for corona graphs. In [12] Lin i Chan...