We present an explicit expression for the number of decompositions of an n-cycle as a product of any two permutations of cycle types given by partitions Ξ» and Β΅. The same expression is also counting the number of unicellular rooted bicolored maps on an orientable surface of genus g with vertex degre
β¦ LIBER β¦
Finding and counting given length cycles
β Scribed by N. Alon; R. Yuster; U. Zwick
- Book ID
- 110547415
- Publisher
- Springer
- Year
- 1997
- Tongue
- English
- Weight
- 684 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0178-4617
No coin nor oath required. For personal study only.
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Let G be a non-trivial connected &,-free graph. If any vertex cut of G contains a veitex v such that G@!(u)) is connected, we prove that G is pancyclic. If G(Z+I(u)) is conaected for any vertex u of G, we prove that G is vertex pancyclic and obtain a polynomial time algorithm for constructing cycles