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-...

Register allocation has long been formulated as a graph coloring problem, coloring the conflict graph with physical registers. Such a formulation does not fully capture the goal of the allocation, which is to minimize the traffic between registers and memory. Linear scan has been proposed as an alternative to graph coloring, but in essence, it can be viewed as a greedy algorithm for graph color...

screw-retained implant restorations have an advantage of predictable retention as well as retrievability, and obviate the risk of excessive sub-gingival cement commonly associated with cement retained implant restorations. screw-retained restorations generally have screw access holes, which can compromise esthetics and weaken the porcelain around the holes. the purpose of this study is to descr...

An incidence of G consists of a vertex and one of its incident edge in G. The incidence coloring problem is a variation of vertex coloring problem. The problem is to find the minimum number (called incidence coloring number) of colors assigned to every incidence of G so that the adjacent incidences are not assigned the same color. In this paper, we propose a linear time algorithm for incidence-...

We investigate k-colorings of the rational n-space, Q, such that any two points at distance one get distinct colors. Two types of colorings are considered: patch colorings where the colors occupy open sets with parts of their boundary, and rigid colorings which uniquely extend from any open subset of Q. We prove that the existence of a patch k-coloring of Q implies the existence of a k-coloring...

Graph coloring was exploited in wireless sensor networks to solve many optimization problems. These problems are related in general to channel assignment. In this paper, we propose to jointly use coloring for routing purposes. We introduce CHRA a coloring based hierarchical routing approach. Coloring is exploited to avoid interferences and also to schedule nodes transmissions to sink. We provid...

The list coloring problem is a variant of vertex coloring where a vertex may be colored only a color from a prescribed set. Several applications of vertex coloring are more appropriately modelled as instances of list coloring and thus we argue that it is an important problem to consider. Regardless of the importance of list coloring, few published algorithms exist for it. In this paper we revie...

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, i.e., partition the vertices to batches which are independent sets, and to assign to each batch a contiguous set of colors, whose size equals to the maximum color requirement of any vertex ...

In this paper, we study the conflict-free coloring of graphs induced by neighborhoods. A coloring of a graph is conflict-free if every vertex has a uniquely colored vertex in its neighborhood. The conflict-free coloring problem is to color the vertices of a graph using the minimum number of colors such that the coloring is conflict-free. We consider both closed neighborhoods, where the neighbor...