A coloring of a graph G is an assignment of colors to the vertices of G in such a way that every pair of adjacent vertices receive different colors. If G admits a coloring using r colors, G is said to be r-colorable, Graph coloring has a number of applications. In many of them, we encounter a situation in which several vertices of G are already colored. We are required to find a coloring which ...

A graph G is called a complete k-partite (k ≥ 2) graph if its vertices can be partitioned into k independent sets V1, . . . , Vk such that each vertex in Vi is adjacent to all the other vertices in Vj for 1 ≤ i < j ≤ k. A complete k-partite graph G is a complete balanced kpartite graph if |V1| = |V2| = · · · = |Vk|. An edge-coloring of a graph G with colors 1, . . . , t is an interval t-colorin...

An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted by rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. It was proved that computing rc(G) is an NP-Hard problem, as well as that even deciding whether a graph has rc(G) =...

The list edge multicoloring problem is a version of edge coloring where every edge e has a list of available colors L(e) and an integer demand x(e). For each e, we have to select x(e) colors from L(e) such that adjacent edges receive disjoint sets of colors. Marcotte and Seymour proved a characterization theorem for list edge multicoloring trees, which can be turned into a polynomial time algor...

The notion of an extremal self-dual code has been introduced in 1 . As Gleason 2 remarks onemay use invariance properties of the weight enumerator of a self-dual code to deduce upper bounds on the minimum distance. Extremal codes are self-dual codes that achieve these bounds. The most wanted extremal code is a binary self-dual doubly even code of length 72 and minimum distance 16. One frequentl...

tion of these two colors to the reproduction process allows Hexachrome to exceed the RGB spectrum in all but the green area of the spectrum (see Figure 1.1). Through this system, offset printers can now reproduce colors beyond the gamut of the monitor and even into the fluorescent and pastel range ( Jeffrey, 1995 p. 46). In addition to this, Hexachrome can accurately reproduce 90% of all PANTON...