The rainbow number of matchings in regular bipartite graphs
نویسندگان
چکیده
منابع مشابه
Rainbow Matchings in Properly Colored Bipartite Graphs
Let G be a properly colored bipartite graph. A rainbow matching of G is such a matching in which no two edges have the same color. Let G be a properly colored bipartite graph with bipartition ( X , Y ) and . We show that if = G k 3 7 max , 4 k X Y , then G has a rainbow coloring of size at least 3 4 k .
متن کاملOn rainbow matchings in bipartite graphs
We present recent results regarding rainbow matchings in bipartite graphs. Using topological methods we address a known conjecture of Stein and show that if Kn,n is partitioned into n sets of size n, then a partial rainbow matching of size 2n/3 exists. We generalize a result of Cameron and Wanless and show that for any n matchings of size n in a bipartite graph with 2n vertices there exists a f...
متن کاملRainbow matchings in bipartite multigraphs
Suppose that k is a non-negative integer and a bipartite multigraph G is the union of N = ⌊ k + 2 k + 1 n ⌋ − (k + 1) matchings M1, . . . ,MN , each of size n. We show that G has a rainbow matching of size n− k, i.e. a matching of size n− k with all edges coming from different Mi’s. Several choices of parameters relate to known results and conjectures. Suppose that a multigraph G is given with ...
متن کاملOn the Number of Perfect Matchings and Hamilton Cycles in e-Regular Non-bipartite Graphs
A graph G = (V,E) on n vertices is super -regular if (i) all vertices have degree in the range [(d − )n, (d + )n], dn being the average degree, and (ii) for every pair of disjoint sets S, T ⊆ V, |S|, |T | ≥ n, e(S, T ) is in the range [(d− )|S||T |, (d+ )|S||T |]. We show that the number of perfect matchings lies in the range [((d−2 )ν n! ν!2ν , (d+ 2 )ν n! ν!2ν ], where ν = n 2 , and the numbe...
متن کاملPerfect Matchings in Õ(n) Time in Regular Bipartite Graphs
We consider the well-studied problem of finding a perfect matching in d-regular bipartite graphs with 2n vertices and m = nd edges. While the best-known algorithm for general bipartite graphs (due to Hopcroft and Karp) takes O(m √ n) time, in regular bipartite graphs, a perfect matching is known to be computable in O(m) time. Very recently, the O(m) bound was improved to O(min{m, n 2.5 lnn d })...
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: Applied Mathematics Letters
سال: 2009
ISSN: 0893-9659
DOI: 10.1016/j.aml.2009.03.019