This paper proposes a new method based on the cultural algorithm to solve graph coloring problem (GCP). Graph coloring problem involves finding the minimum number of colors for coloring the graph vertices such that adjacent vertices have distinct colors. In this paper various components of cultural algorithm have been implemented to solve GCP with a self adaptive behavior in an efficient manner...

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. A graph G is s-degenerated for a positive integer s if G can be reduced to a trivial graph by successive removal of vertices with degree ≤ s. We prove that an s-degenerated graph G has a total coloring with ∆ + 1 colors if the...

This paper presents an extraction and expansion approach for the graph coloring problem. The extraction phase transforms a large graph into a sequence of progressively smaller graphs by removing large independent sets from the graph. The expansion phase starts by generating an approximate coloring for the smallest graph in the sequence. Then it expands the smallest graph by progressively adding...

This paper aims to give a focused introduction to algebraic graph theory accessible to mathematically mature undergraduates. We will begin by giving some standard definitions, then expanding our focus to specifically study properties of graph homomorphisms in the context of constraint satisfaction problems (graph coloring in disguise). In particular, we will be discussing the idea of graph colo...

This paper considers a different version of the parallel machines scheduling problem in which the parallel jobs simultaneously requirea pre-specifiedjob-dependent number of machines when being processed.This relaxation departs from one of the classic scheduling assumptions. While the analytical conditions can be easily statedfor some simple models, a graph model approach is required when confli...

For example is a chromatic number with the smallest integer so that graph has true vertex coloring k color. Chromatic still an interesting study which being studied for its development through coloring. Graph special case of labeling. Labeling here means, giving color to points at certain limit no two vertices have same This aims calculate in several classes graphs including , Based on results ...

This paper is concerned with algorithms and complexity results for defective coloring, where a defective (k; d)-coloring is a k coloring of the vertices of a graph such that each vertex is adjacent to at most d-self-colored neighbors. First, (2; d) coloring is shown NP-complete for d 1, even for planar graphs, and (3; 1) coloring is also shown NP-complete for planar graphs (while there exists a...

Some situations concerning cost allocation are formulated as combinatorial optimization games. We consider a minimum coloring game and a minimum vertex cover game. For a minimum coloring game, Deng{Ibaraki{Nagamochi 1] showed that deciding the core nonemptiness of a given minimum coloring game is NP-complete, which implies that a good characterization of balanced minimum coloring games is unlik...

An edge-weighting of a graph is called vertex-coloring if the weighted degrees yield proper vertex coloring graph. It conjectured that for every without isolated edge, with set {1,2,3} exists. In this note, we show statement true weight {1,2,3,4}.