Concepts inFinding the chromatic number by means of critical graphs
Critical graph
In general the notion of criticality can refer to any measure. But in graph theory, when the term is used without any qualification, it almost always refers to the chromatic number of a graph. Critical graphs are interesting because they are the minimal members in terms of chromatic number, which is a very important measure in graph theory. More precise definitions follow. A vertex or an edge is a critical element of a graph G if its deletion would decrease the chromatic number of G.
more from Wikipedia
Graph coloring
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring.
more from Wikipedia
DIMACS
The Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) is a collaboration between Rutgers University, Princeton University, and the research firms AT&T, Bell Labs, Telcordia, and NEC. It was founded in 1989 with money from the National Science Foundation. Its offices are located on the Rutgers campus, and 250 members from the six institutions form its permanent members.
more from Wikipedia
Random graph
In mathematics, a random graph is a graph that is generated by some random process. The theory of random graphs lies at the intersection between graph theory and probability theory, and studies the properties of typical random graphs.
more from Wikipedia
Glossary of graph theory
Graph theory is a growing area in mathematical research, and has a large specialized vocabulary. Some authors use the same word with different meanings. Some authors use different words to mean the same thing. This page attempts to describe current usage.
more from Wikipedia
Partially ordered set
In mathematics, especially order theory, a partially ordered set (or poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation that indicates that, for certain pairs of elements in the set, one of the elements precedes the other.
more from Wikipedia
Graph (mathematics)
In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics.
more from Wikipedia