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...

An L(2, 1)-coloring of a graph G is a coloring of G’s vertices with integers in {0, 1, . . . , k} so that adjacent vertices’ colors differ by at least two and colors of distance-two vertices differ. We refer to an L(2, 1)-coloring as a coloring. The span λ(G) of G is the smallest k for which G has a coloring, a span coloring is a coloring whose greatest color is λ(G), and the hole index ρ(G) of...

If a graph G contains no subgraph isomorphic to some graph H, then G is called H-free. A coloring of a graph G = (V,E) is a mapping c : V → {1, 2, . . .} such that no two adjacent vertices have the same color, i.e., c(u) 6= c(v) if uv ∈ E; if |c(V )| ≤ k then c is a k-coloring. The Coloring problem is to test whether a graph has a coloring with at most k colors for some integer k. The Precolori...

Golovach, Paulusma and Song (Inf. Comput. 2014) asked to determine the parameterized complexity of following problems by k: (1) Given a graph G, clique modulator D (a is set vertices, whose removal results in clique) size k for list L(v) colors every v ∈ V(G), decide whether G has proper coloring; (2) pre-coloring λ_P: X → Q ⊆ λ_P can be extended coloring using only from Q. For Problem 1 we des...

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...

given a graph $g$, the total dominator coloring problem seeks aproper coloring of $g$ with the additional property that everyvertex in the graph is adjacent to all vertices of a color class. weseek to minimize the number of color classes. we initiate to studythis problem on several classes of graphs, as well as findinggeneral bounds and characterizations. we also compare the totaldominator chro...

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 ? (...

In this paper some new results on the acyclic-edge coloring , f -edge coloring, g-edge cover coloring, (g, f )-coloring and equitable edge-coloring of graphs are introduced. In particular, some new results related to the above colorings obtained by us are given. Some new problems and conjectures are presented.

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...