Coloring of a graph is an assignment of colors either to the edges of the graph G, or to vertices, or to maps in such a way that adjacent edges/vertices/maps are colored differently. We consider the problem of coloring graphs by using webMathematica which is the new web-based technology. In this paper, we describe some web-based interactive examples on graph coloring with webMathematica.

We study a three-dimensional analogue to the well-known graph visualization approach known as arc diagrams. We provide several algorithms that achieve good angular resolution for 3D arc diagrams, even for cases when the arcs must project to a given 2D straight-line drawing of the input graph. Our methods make use of various graph coloring algorithms, including an algorithm for a new coloring pr...

We consider the graph coloring game, a game in which two players take turns properly vertices of graph, with one player attempting to complete proper coloring, and other prevent coloring. show that if G has number each bicolored subgraph is bounded, then chromatic bounded. As corollary this result, we for graphs 1 2 bounded number, Cartesian product □ answering question X. Zhu. also obtain an u...

The distance-2 graph coloring problem aims at partitioning the vertex set of a graph into the fewest sets consisting of vertices pairwise at distance greater than two from each other. Application examples include numerical optimization and channel assignment. We present the first distributed-memory heuristic algorithm for this NP-hard problem. Parallel speedup is achieved through graph partitio...

A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes, and the b-chromatic number of a graph G is the largest integer k such that G admits a b-coloring with k colors. A graph is b-perfect if the b-chromatic number is equal to the chromatic number for every induced subgraph of G. We prove that a graph is ...

A linear coloring of a graph is a proper coloring of the vertices of the graph so that each pair of color classes induce a union of disjoint paths. In this paper, we prove that for every connected graph with maximum degree at most three and every assignment of lists of size four to the vertices of the graph, there exists a linear coloring such that the color of each vertex belongs to the list a...

A k-edge-weighting w of a graph G is an assignment of an integer weight, w(e) ∈ {1, . . . , k}, to each edge e. An edge weighting naturally induces a vertex coloring c by defining c(u) = ∑ u∼e w(e) for every u ∈ V (G). A k-edge-weighting of a graph G is vertexcoloring if the induced coloring c is proper, i.e., c(u) ≠ c(v) for any edge uv ∈ E(G). Given a graph G and a vertex coloring c0, does th...

Abs t r ac t . In an edge-coloring of a graph G = (V, E) each color appears around each vertex at most once. An f-coloring is a generalization of an edge-coloring in which each color appears around each vertex v at most f(v) times where f is a function assigning a natural number f(v) e N to each vertex v E V. In this paper we first give a simple reduction of the f-coloring problem to the ordina...

A set coloring α of a graph G is defined as an assignment of distinct subsets of a finite set X of colors to the vertices of G such that all the colors of the edges which are obtained as the symmetric differences of the sets assigned to their end-vertices are distinct. Additionally, if all the sets on the vertices and edges of G form the set of all nonempty subsets of X, then the coloring α is ...