In parallel computing, a valid graph coloring yields a lock-free processing of the colored tasks, data points, etc., without expensive synchronization mechanisms. However, coloring is not free and the overhead can be significant. In particular, for the bipartite-graph partial coloring (BGPC) and distance-2 graph coloring (D2GC) problems, which have various use-cases within the scientific comput...

For a fixed simple digraph F and given D , an - free k -coloring of is vertex-coloring in which no induced copy monochromatic. We study the complexity deciding for whether admits -free -coloring. Our main focus on restriction problem to planar input digraphs, where it only interesting cases ? { 2 3 } . From known results follows that every whose underlying graph not forest, 2-coloring, with ? (...

Late binding and subtyping create run-time overhead for object-oriented languages. Dynamic typing and multiple inheritance create even more overhead. Static typing and single inheritance lead to two major invariants—of reference and position—that make the implementation as efficient as possible. Coloring is a technique that preserves these invariants for dynamic typing or multiple inheritance a...

A total coloring of a graph G is a coloring of all elements of G, i.e., vertices and edges, in such a way that no two adjacent or incident elements receive the same color. Let L(x) be a set of colors assigned to each element x of G. Then a list total coloring of G is a total coloring such that each element x receives a color contained in L(x). The list total coloring problem asks whether G has ...

The max-coloring problem is to compute a legal coloring of the vertices of a graph G = (V,E) with vertex weights w such that ∑k i=1 maxv∈Ci w(vi) is minimized, where C1, . . . , Ck are the various color classes. For general graphs, max-coloring is as hard as the classical vertex coloring problem, a special case of the former where vertices have unit weight. In fact, in some cases it can even be...

A basic randomized coloring procedure has been used in probabilistic proofs to obtain remarkably strong results on graph coloring. These results include the asymptotic version of the List Coloring Conjecture due to Kahn, the extensions of Brooks’ Theorem to sparse graphs due to Kim and Johansson, and Luby’s fast parallel and distributed algorithms for graph coloring. The most challenging aspect...