This paper surveys recent development of concepts related to coloring signed graphs. Various approaches are presented and discussed.

This thesis studies both several extremal problems about coloring of graphs and a labeling problem on graphs. We consider colorings of graphs that are either embeddable in the plane or have low maximum degree. We consider three problems: coloring the vertices of a graph so that no adjacent vertices receive the same color, coloring the edges of a graph so that no adjacent edges receive the same ...

Given a graph G, b coloring seeks proper of G with the descriptive property that every color class in contains dominating vertex. We have to minimize number colors coloring. In this paper, we show how chromatic and b-chromatic changes operators relation between has been explored.

In this paper, we present a deterministic \(\mathsf {CONGEST} \) algorithm to compute an O ( kΔ )-vertex coloring in Δ / k ) + log * n rounds, where is the maximum degree of network graph and ≥ 1 can be freely chosen. The extremely simple: Each node locally computes sequence colors then it tries from batches size . Our subsumes many important results history distributed as special cases, includ...

In this paper we propose a deterministic parallel graph coloring algorithm that enables Multi-Coloring in parallel for sparse undirected graphs by coarse-grained segmentation and auxiliary graph coloring. The proposed algorithm is implemented and tested on standard problem instances from engineering applications and benchmarked against various relevant deterministic graph coloring algorithms. Q...

Let Γ be directed strongly connected finite graph of uniform outdegree (constant outdegree of any vertex) and let some coloring of edges of Γ turn the graph into deterministic complete automaton. Let the word s be a word in the alphabet of colors (considered also as letters) on the edges of Γ and let Γs be a mapping of vertices Γ. A coloring is called k-synchronizing if for any word t |Γt| ≥ k ...

We studied the relative performance of genetic algorithms on coloring a dynamic graph for di↵erent graph and algorithm conditions. Graph coloring is a well-studied NP-complete problem with a wide range of applications in scheduling and assignment problems, while dynamic graphs are a natural way to model a diverse range of dynamic systems, from register allocation to mobile ad-hoc networks. Colo...