chromatic number

Noun

 * 1)  The smallest number of colours needed to colour a given graph (i.e., to assign a colour to each vertex such that no two vertices connected by an edge have the same colour).
 * 2) * 2004, Monia Discepoli, Ivan Gerace, Riccardo Mariani, Andrea Remigi, A Spectral Technique to Solve the Chromatic Number Problem in Circulant Graphs, Antonio Laganà, et al. (editors), Computational Science and Its Applications, ICCSA 2004: International Conference, Proceedings, Part 3, Springer, 3045, page 745,
 * The  CHROMATIC NUMBER  is the minimum number of colors by means of which it is possible to color a graph in such a way that each vertex has a different color with respect to the adjacent vertices. Such a problem is an NP-hard problem [14] and [it] is even hard to obtain a good approximation of the solution in a polynomial time [17]. Although in a lot of computational problems the cost decreases when these problems are restricted to circulant graphs [6, 9], the  CHROMATIC NUMBER  problem is NP-hard even restrecting [sic] to circulant graphs [9]. Moreover the problem of finding a good approximation of the  CHROMATIC NUMBER  problem on circulant graphs is also NP-hard.
 * 1) * 2009, Gary Chartrand, Ping Zhang, Chromatic Graph Theory, Taylor & Francis Group (CRC Press / Chapman & Hall), page 149,
 * There is no general formula for the chromatic number of a graph. Consequently, we will often be concerned and must be content with (1) determining the chromatic number of some classes of interest and (2) determining upper and/or lower bounds for the chromatic number of a graph.
 * 1) * 2009, Gary Chartrand, Ping Zhang, Chromatic Graph Theory, Taylor & Francis Group (CRC Press / Chapman & Hall), page 149,
 * There is no general formula for the chromatic number of a graph. Consequently, we will often be concerned and must be content with (1) determining the chromatic number of some classes of interest and (2) determining upper and/or lower bounds for the chromatic number of a graph.

Usage notes

 * Not to be confused with (aka ), which is the equivalent minimum number for an edge colouring.
 * The chromatic number of a graph $$G$$ is often denoted $$\chi(G)$$.

Translations

 * Hungarian:
 * Icelandic: litatala
 * Italian: numero cromatico
 * Spanish: número cromático