Simion, R., Trees with l-factors and oriented trees, Discrete Mathematics 88 (1991) 93-104. In this paper we present some results on trees with a l-factor: generating functions and asymptotics for the number of such trees, labeled, rooted, planted and unlabeled. We show that almost all trees with a
Factors of trees
β Scribed by Tao Wang
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 608 KB
- Volume
- 131
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
Two criteria for a tree to have an f-factor and (g, f)-factors are presented, respectively. They simplify, respectively, Tutte's condition for a graph to havef-factors and Lov~sz's condition for a graph to have (g,f)-factors.
An O(j V(T)/) algorithm and an O(l V(T)I') algorithm for f-factor and (g, f)-factor problems for trees are given, respectively.
π SIMILAR VOLUMES
## Abstract A tree is even if its edges can be colored in two colors so that the monochromatic subgraphs are isomorphic. All even trees of maximum degree 3 in which no two vertices of degrees 1 or 3 are adjacent are determined. It is also shown that, for every __n__, there are only finitely many tr
## Abstract In this paper we exhibit a class of trees with the property that if __T__~__k__~ is a tree on __k__ vertices that belongs to this class, then necessary and sufficient conditions for __K__~__n__~ to have a __T__~__k__~βfactorization are simply __n__ = 0 (mod k) and __n__ = 1 (mod 2(__k__
We provide a bijection between the set of factorizations, that is, ordered (n -1)tuples of transpositions in S n whose product is (12...n), and labelled trees on n vertices. We prove a refinement of a theorem of J. DΓ©nes (1959, Publ. Math. Inst. Hungar. Acad. Sci. 4, 63-71) that establishes new tree