Batch scheduling of conflicting jobs is modeled by batch coloring of a graph. Given an undirected graph and the number of colors required by each vertex, we need to find a proper batch coloring of the graph, namely, to partition the vertices to batches which are independent sets and assign to each batch a contiguous set of colors, whose size is equal to the maximum color requirement of any vert...

Given a nite directed graph, a coloring of its edges turns the graph into a nite-state automaton. A k-synchronizing word of a deterministic automaton is a word in the alphabet of colors at its edges that maps the state set of the automaton at least on k-element subset. A coloring of edges of a directed strongly connected nite graph of a uniform outdegree (constant outdegree of any vertex) is k-...

Processor cache memory management is a challenging issue as it deeply impact performances and power consumption of electronic devices. It has been shown that allocating data structures to memory for a given application (as MPEG encoding, filtering or any other signal processing application) can be modeled as a minimum k-weighted graph coloring problem, on the so-called conflict graph. The graph...

This article studies a degree-bounded generalization of independent sets called co-k-plexes. Constant factor approximation algorithms are developed for the maximum co-k-plex problem on unit-disk graphs. The related problem of minimum co-k-plex coloring that generalizes classical vertex coloring is also studied in the context of unit-disk graphs. We extend several classical approximation results...

The problem of online coloring an unknown graph is known to be hard. Here we consider the problem of online coloring in the relaxed situation where the input must be isomorphic to a given known graph. All that foils a computationally powerful player is that it is not known to which sections of the graph the vertices to be colored belong. We show that the performance ratio of any online coloring...

A synchronizing word of a deterministic automaton is a word in the alphabet of colors (considered as letters) of its edges that maps the automaton to a single state. A coloring of edges of a directed graph is synchronizing if the coloring turns the graph into a deterministic finite automaton possessing a synchronizing word. The road coloring problem is the problem of synchronizing coloring of a...

The graph coloring problem is a notoriously hard problem, for which we do not have efficient algorithms. A coloring of a graph is an assignment of colors to its vertices such that the end points of every edge have different colors. A k-coloring is a coloring that uses at most k distinct colors. The graph coloring problem is to find a coloring that uses the minimum number of colors. Given a 3-co...

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...

A graph is H-free if it does not contain an induced subgraph isomorphic to the graph H. The graph Pk denotes a path on k vertices. The `-Coloring problem is the problem to decide whether a graph can be colored with at most ` colors such that adjacent vertices receive different colors. We show that 4-Coloring is NP-complete for P8free graphs. This improves a result of Le, Randerath, and Schierme...