Vertex-distinquishing edge-colorings of linear forests

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

Dynamic Algorithms for Graph Coloring

We design fast dynamic algorithms for proper vertex and edge colorings in a graph undergoing edge insertions and deletions. In the static setting, there are simple linear time algorithms for (∆ + 1)vertex coloring and (2∆ − 1)-edge coloring in a graph with maximum degree ∆. It is natural to ask if we can efficiently maintain such colorings in the dynamic setting as well. We get the following th...

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...

Nowhere-harmonic Colorings of Graphs

Abstract. Proper vertex colorings of a graph are related to its boundary map, also called its signed vertex-edge incidence matrix. The vertex Laplacian of a graph, a natural extension of the boundary map, leads us to introduce nowhere-harmonic colorings and analogues of the chromatic polynomial and Stanley’s theorem relating negative evaluations of the chromatic polynomial to acyclic orientatio...

Vertex-, edge-, and total-colorings of Sierpinski-like graphs

Vertex-colorings, edge-colorings and total-colorings of the Sierpiński gasket graphs Sn, the Sierpiński graphs S(n, k), graphs S (n, k), and graphs S(n, k) are considered. In particular, χ′′(Sn), χ (S(n, k)), χ(S(n, k)), χ(S(n, k)), χ(S(n, k)), and χ(S(n, k)) are determined.