The graph coloring problem (GCP) is one of the most interesting, studied and difficult combinatorial optimization problems. That is why, several approaches were developed for solving this problem, including exact approaches, heuristic approaches, metaheuristics and hybrid approaches. In this paper, we try to solve the graph coloring problem using a new approach based on the quantum inspired cuc...

It was conjectured in [S. Akbari, F. Khaghanpoor, and S. Moazzeni. Colorful paths in vertex coloring of graphs. Preprint] that, if G is a connected graph distinct from C7, then there is a χ(G)-coloring of G in which every vertex v ∈ V (G) is an initial vertex of a path P with χ(G) vertices whose colors are different. In [S. Akbari, V. Liaghat, and A. Nikzad. Colorful paths in vertex coloring of...

Many classes of graphs where the vertex coloring problem is polynomially solvable are known, the most prominent being the class of perfect graphs. However, the list-coloring problem is NP-complete for many subclasses of perfect graphs. In this work we explore the complexity boundary between vertex coloring and list-coloring on such subclasses of perfect graphs, where the former admits polynomia...

To investigate the exploitation and contamination by self-propagating Internet worms, a provenanceaware tracing mechanism is highly desirable. Provenance unawareness causes difficulties in fast and accurate identification of a worm’s break-in point (namely, a remotely-accessible vulnerable service running in the infected host), and incurs significant log data inspection overhead. This paper pre...

Dynamic irregular triangulated meshes are used in adaptive grid partial diierential equation (PDE) solvers, and in simulations of random surface models of quantum gravity in physics and cell membranes in biology. Parallel algorithms for random surface simulations and adaptive grid PDE solvers require coloring of the triangulated mesh, so that neighboring vertices are not updated simultaneously....

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...

Motivated by the definition of linear coloring on simplicial complexes, recently introduced in the context of algebraic topology [9], and the framework through which it was studied, we introduce the linear coloring on graphs. We provide an upper bound for the chromatic number χ(G), for any graph G, and show that G can be linearly colored in polynomial time by proposing a simple linear coloring ...

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...

Motivated by the notion of linear coloring on simplicial complexes, recently introduced in the context of algebraic topology, and the framework through which it was studied, we introduce the colinear coloring on graphs. We provide an upper bound for the chromatic number χ(G), for any graph G, and show that G can be colinearly colored in polynomial time by proposing a simple algorithm. The colin...