A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and it is denoted by χ=(G). In this paper the problem of determinig χ= for coronas of cubic graphs is studied. Although the prob...

An acyclic coloring of a graph is a proper coloring such that any two color classes induce a forest. A star coloring of a graph is an acyclic coloring with the further restriction that the forest induced by any two color classes is a disjoint collection of stars. We consider the behavior of these problems when restricted to certain classes of graphs. In particular, we give characterizations of ...

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...

Extending previous NP-completeness results for the harmonious coloring problem and the pair-complete coloring problem on trees, bipartite graphs and cographs, we prove that these problems are also NP-complete on connected bipartite permutation graphs. We also study the k-path partition problem and, motivated by a recent work of Steiner [G. Steiner, On the k-path partition of graphs, Theoret. Co...

It is shown that, for any > 0, every graph of maximum degree ∆ permits a conflict-free coloring with at most log ∆ colors, that is, a coloring with the property that the neighborhood N(v) of any vertex v, contains an element whose color differs from the color of any other element of N(v). We give an efficient deterministic algorithm to find such a coloring, based on an algorithmic version of th...

We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of finite families of translates and homothets of a convex body in R.

Register allocation, i.e., the task of assigning processor registers to local variables and temporary values, is one of the most important compiler optimizations. A vast amount of research has led to algorithms ranging from simple and fast heuristics to optimal algorithms with exponential time complexity. Because the problem is known to be NP-complete [2], algorithms must balance the time neces...

Low-treedepth colorings are an important tool for algorithms that exploit structure in classes of bounded expansion; they guarantee subgraphs that use few colors are guaranteed to have bounded treedepth. These colorings have an implicit tradeoff between the total number of colors used and the treedepth bound, and prior empirical work suggests that the former dominates the run time of existing a...

We introduce a new class of compiler heuristics: hybrid optimizations. Hybrid optimizations choose dynamically at compile time which optimization algorithm to apply from a set of different algorithms that implement the same optimization. They use a heuristic to predict the most appropriate algorithm for each piece of code being optimized. Specifically, we construct a hybrid register allocator t...

We give a linear-time algorithm to decide 3-colorability (and find a 3coloring, if it exists) of quadrangulations of a fixed surface. The algorithm also allows to prescribe the coloring for a bounded number of vertices.