A result on 2k-cycle-free bipartite graphs
نویسنده
چکیده
Let G be a bipartite graph with vertex parts of orders N and M , and X edges. I prove that if G has no cycles of length 2l, for all l ∈ [2, 2k], and N ≥ M , then X < M 1 2 N k+1 2k + O(N).
منابع مشابه
Properties of Certain Families of 2k-Cycle-Free Graphs
Let v = v(G) and e = e(G) denote the order and size of a simple graph G, respectively. Let G = {Gi}i≥1 be a family of simple graphs of magnitude r > 1 and constant λ > 0, i.e. e(Gi) = (λ+ o(1))v(Gi), i→∞. For any such family G whose members are bipartite and of girth at least 2k + 2, and every integer t, 2 ≤ t ≤ k − 1, we construct a family G̃t of graphs of same magnitude r, of constant greater ...
متن کاملA Note on Bipartite Graphs without 2k-Cycles
We address the question of the maximum number ex(m,n, C2k) of edges in an m by n bipartite graph without a cycle of length 2k. We prove that for each k ≥ 2, ex(m,n, C2k) ≤ (2k − 3) [ (mn) k+1 k + m + n ] if k is odd. (2k − 3) [ m k+2 k n 1 2 + m + n ] if k is even.
متن کاملMixed cycle-E-super magic decomposition of complete bipartite graphs
An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ΣνεV(H) f(v) + ΣeεE(H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥ ...
متن کاملA generalization of Villarreal's result for unmixed tripartite graphs
In this paper we give a characterization of unmixed tripartite graphs under certain conditions which is a generalization of a result of Villarreal on bipartite graphs. For bipartite graphs two different characterizations were given by Ravindra and Villarreal. We show that these two characterizations imply each other.
متن کاملRestricted 2 { factors in Bipartite
The k{restricted 2{factor problem is that of nding a spanning subgraph consisting of disjoint cycles with no cycle of length less than or equal to k. It is a generalization of the well known Hamilton cycle problem and is equivalent to this problem when n 2 k n ? 1. This paper considers necessary and suucient conditions, algorithms, and polyhedral conditions for 2{factors in bipartite graphs and...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Australasian J. Combinatorics
دوره 32 شماره
صفحات -
تاریخ انتشار 2005