Regular Spanning Subgraphs of Bipartite Graphs of High Minimum Degree
نویسنده
چکیده
Let G be a simple balanced bipartite graph on 2n vertices, δ = δ(G)/n, and ρ0 = δ+ √ 2δ−1 2 . If δ ≥ 1/2 then G has a ⌊ρ0n⌋-regular spanning subgraph. The statement is nearly tight.
منابع مشابه
Existence of Spanning ℱ-Free Subgraphs with Large Minimum Degree
Let F be a family of graphs and let d be large enough. For every d-regular graph G, we study the existence of a spanning F -free subgraph of G with large minimum degree. This problem is wellunderstood if F does not contain bipartite graphs. Here we provide asymptotically tight results for many families of bipartite graphs such as cycles or complete bipartite graphs. To prove these results, we s...
متن کاملThe distinguishing chromatic number of bipartite graphs of girth at least six
The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. The distinguishing chromatic number $chi_{D}(G)$ of $G$ is defined similarly, where, in addition, $f$ is assumed to be a proper labeling. We prove that if $G$ is a bipartite graph of girth at least six with the maximum ...
متن کاملLarge Subgraphs without Short Cycles
We study two extremal problems about subgraphs excluding a family F of graphs. i) Among all graphs with m edges, what is the smallest size f(m,F) of a largest F–free subgraph? ii) Among all graphs with minimum degree δ and maximum degree ∆, what is the smallest minimum degree h(δ,∆,F) of a spanning F– free subgraph with largest minimum degree? These questions are easy to answer for families not...
متن کاملRIMS-1826 Approximation Algorithms for the Minimum 2-edge Connected Spanning Subgraph Problem and the Graph-TSP in Regular Bipartite Graphs via Restricted 2-factors By
In this paper, we address the minimum 2-edge connected spanning subgraph problem and the graph-TSP in regular bipartite graphs. For these problems, we present new approximation algorithms, each of which finds a restricted 2-factor close to a Hamilton cycle in the first step. We first prove that every regular bipartite graph of degree at least three has a square-free 2-factor. This immediately l...
متن کاملBalanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations
A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 14 شماره
صفحات -
تاریخ انتشار 2007