✦ LIBER ✦
A generalized chromatic polynomial, acyclic orientations with prescribed sources and sinks, and network reliability
✍ Scribed by J. Rodriguez; A. Satyanarayana
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 753 KB
- Volume
- 112
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
Suppose G =(V, E) is a graph and K, K', K" are subsets of V such that K sK'nK".
We introduce and study a polynomial P(G, K, K', K"; I.) in i. This polynomial coincides with the classical chromatic polynomial P(G; 1) when K = V. The results of this paper generalize Whitney's characterizations of the coefficients of P(G; i) and the work of Stanley on acyclic orientations.
Furthermore, we establish a connection between a family of polynomials associated with network reliability and a family of polynomials associated with P(G