## Abstract The upper bound for the harmonious chromatic number of a graph given by Zhikang Lu and by C. McDiarmid and Luo Xinhua, independently (__Journal of Graph Theory__, 1991, pp. 345–347 and 629–636) and the lower bound given by D. G. Beane, N. L. Biggs, and B. J. Wilson (__Journal of Graph T
Tight bounds on the chromatic sum of a connected graph
✍ Scribed by Carsten Thomassen; Paul Erdös; Yousef Alavi; Paresh J. Malde; Allen J. Schwenk
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 236 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
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## Abstract Bounds on the sum and product of the chromatic numbers of __n__ factors of a complete graph of order __p__ are shown to exist. The well‐known theorem of Nordhaus and Gaddum solves the problem for __n__ = 2. Strict lower and some upper bounds for any __n__ and strict upper bounds for __n