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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Cycle polynomials


Author: F. K. Hwang
Journal: Proc. Amer. Math. Soc. 83 (1981), 215-219
MSC: Primary 05C30; Secondary 05C38
DOI: https://doi.org/10.1090/S0002-9939-1981-0620017-X
MathSciNet review: 620017
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Abstract: Let $ G$ be a graph consisting of $ m$ vertex-disjoint cycles with possibly different numbers of vertices on each cycle. We want to count the number of ways of selecting $ k$ vertices in $ G$ such that there are exactly $ l$ edges spanned by these $ k$ vertices. For $ m = 1$, the problem is equivalent to the Whitworth bracelet problem with two colors and a closed-form solution is known. In this paper we show that the solution for the many-cycle case can be written as a sum of the solutions for single-cycle cases.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0620017-X
Keywords: Whitworth runs, Jablonski runs, Whitworth bracelet problem
Article copyright: © Copyright 1981 American Mathematical Society