On chromatic and dichromatic sum equations

✍ Scribed by Yanpei Liu

• Book ID: 103056830
• Publisher: Elsevier Science
• Year: 1990
• Tongue: English
• Weight: 609 KB
• Volume: 84
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(90)90372-o

✦ Synopsis

This paper provides firstly an exposition on the theory of chromatic sums for rooted planar triangulations founded by W.T. Tutte. Then, the generalization of the theory for rooted nonseparable planar maps is described. Further, a functional equation of the dichromatic sum functions for rooted nonseparable planar maps is also established by using the same decomposition lemmas as those in the chromatic case. However, it seems that the equations obtained here can not be directly derived from the dichromatic sum equation for rooted general planar maps which was discovered by W.T. Tutte as well.