The harmonious chromatic number of a graph is the least number of colours in a vertex colouring such that each pair of colours appears on at most one edge. The achromatic number of a graph is the greatest number of colours in a vertex colouring such that each pair of colours appears on at least one edge. This paper is a survey of what is known about these two parameters, in particular we look at upper and lower bounds, special classes of graphs and complexity issues.
|Title of host publication||Surveys in combinatorics, 1997|
|Editors||R. A. Bailey|
|Publisher||Cambridge University Press|
|Number of pages||36|
|Publication status||Published - 1997|
|Name||London Mathematical Society Lecture Note Series|
Edwards, K. (1997). The harmonious chromatic number and the achromatic number. In R. A. Bailey (Ed.), Surveys in combinatorics, 1997 (pp. 13-48). (London Mathematical Society Lecture Note Series; Vol. 241). Cambridge University Press. https://doi.org/10.1017/CBO9780511662119.003