Characterizing minimally 1-factorable r-regular bipartite graphs
نویسندگان
چکیده
منابع مشابه
Characterizing minimally n-extendable bipartite graphs
In this paper, it is proved that let G be a bipartite graph with bipartition (X, Y ) and with a perfect matching M , let G be an n-extendable graph, then G is minimally n-extendable if and only if, for any two vertices x ∈ X and y ∈ Y such that xy ∈ E(G), there are exactly n internally disjoint (x, y) M-alternating paths P1, P2, . . . , Pn such that Pi (1 i n) starts and ends with edges in E(G)...
متن کاملOn determinants and permanents of minimally 1-factorable cubic bipartite graphs
A minimally 1-factorable cubic bigraph is a graph in which every 1-factor lies in precisely one 1-factorization. The author investigates determinants and permanents of such graphs and, in particular, proves that the determinant of any minimally 1-factorable cubic bigraph of girth 4 is 0.
متن کاملCounting 1-Factors in Regular Bipartite Graphs
perfect matchings. (A perfect matching or 1-factor is a set of disjoint edges covering all vertices.) This generalizes a result of Voorhoeve [11] for the case k = 3, stating that any 3-regular bipartite graph with 2n vertices has at least ( 4 3) n perfect matchings. The base in (1) is best possible for any k: let αk be the largest real number such that any k-regular bipartite graph with 2n vert...
متن کاملq - regular bipartite graphs
An explicit construction of a family of binary LDPC codes called LU(3, q), where q is a power of a prime, was recently given. A conjecture was made for the dimensions of these codes when q is odd. The conjecture is proved in this note. The proof involves the geometry of a 4-dimensional symplectic vector space and the action of the symplectic group and its subgroups.
متن کاملRegular bipartite graphs are antimagic
A labeling of a graph G is a bijection from E(G) to the set {1, 2, . . . , |E(G)|}. A labeling is antimagic if for any distinct vertices u and v, the sum of the labels on edges incident to u is different from the sum of the labels on edges incident to v. We say a graph is antimagic if it has an antimagic labeling. In 1990, Ringel conjectured that every connected graph other than K2 is antimagic...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00189-3