Parity vertex colorings of binomial trees

Strong parity vertex coloring of plane graphs

Czap and Jendrol’ introduced the notions of strong parity vertex coloring and the corresponding strong parity chromatic number χs. They conjectured that there is a constant bound K on χs for the class of 2-connected plane graphs. We prove that the conjecture is true with K = 97, even with an added restriction to proper colorings. Next, we provide simple examples showing that the sharp bound is ...

On the Defining Number of (2n - 2)-Vertex Colorings of Kn x Kn

Conflict-Free Colorings - Of Graphs and Hypergraphs - Diploma-Thesis of

Conflict-free colorings are known as vertex-colorings of hypergraphs. In such a coloring each hyperedge contains a vertex whose color is not assigned to any other vertex within this edge. In this thesis the notion of conflict-free colorings is translated to edge-colorings of graphs. For graphs G and H a conflict-free coloring of G ensures an edge of unique color in each copy of H in G. The mini...

Extremal H-colorings of trees and 2-connected graphs

For graphs G and H, an H-coloring of G is an adjacency preserving map from the vertices of G to the vertices of H. H-colorings generalize such notions as independent sets and proper colorings in graphs. There has been much recent research on the extremal question of finding the graph(s) among a fixed family that maximize or minimize the number of H-colorings. In this paper, we prove several res...

Channel Assignment on Strongly-Simplicial Graphs

Given a vector ( 1; 2; : : : ; t) of non increasing positive inte gers, and an undirected graph G = (V;E), an L( 1; 2; : : : ; t)-coloring of G is a function f from the vertex set V to a set of nonnegative inte gers such that jf(u) f(v)j i, if d(u; v) = i; 1 i t; where d(u; v) is the distance (i.e. the minimum number of edges) between the vertic es u and v. This paper presents e cient algorithm...