Series-parallel orientations preserving the cycle-radius
نویسندگان
چکیده
Let G be an undirected 2-edge connected graph with nonnegative edge weights and a distinguished vertex z. For every node consider a shortest cycle containing this node and z in G. The cycle-radius of G is the maximum length of a cycle in this set. Let H be a directed graph obtained by directing the edges of G. The cycle-radius of H is similarly defined except that cycles are replaced by directed closed walks. We prove that there exists for every nonnegative edge weight function an orientation H of G whose cycle-radius equals that of G if and only if G is series-parallel.
منابع مشابه
Constructing even radius tightly attached half-arc-transitive graphs of valency four
A finite graph X is half-arc-transitive if its automorphism group is transitive on vertices and edges, but not on arcs. When X is tetravalent, the automorphism group induces an orientation on the edges and a cycle of X is called an alternating cycle if its consecutive edges in the cycle have opposite orientations. All alternating cycles of X have the same length and half of this length is calle...
متن کاملLinear Maps Preserving Invertibility or Spectral Radius on Some $C^{*}$-algebras
Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $varphi:Arightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.
متن کاملNote on inseparability graphs of matroids having exactly one class of orientations
The inseparability graph of an oriented matroid is an invariant of its class of orientations. When an orientable matroid has exactly one class of orientations the inseparability graph of all its orientations is in fact determined by its non-oriented underlying matroid. From this point of view it is natural to ask if inseparability graphs can be used to characterize matroids which have exactly o...
متن کاملFingertip Radius Effect of an on-Surface-Manipulated Object
Cooperative arms are two or more arms in series which assume the structure of a parallel robot on account of gripping an intermediary object, and are commonly used in accurate assembly industries, coaxialization, movement of object, etc. Gripping an intermediary object is one of the complicated subjects in analysis of cooperative arms, whose analysis is mostly dependent upon the manner the obje...
متن کاملThe Merino-Welsh conjecture holds for series-parallel graphs
The Merino-Welsh conjecture asserts that the number of spanning trees of a graph is no greater than the maximum of the numbers of totally cyclic orientations and acyclic orientations of that graph. We prove this conjecture for the class of series-parallel graphs.
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:
- Inf. Process. Lett.
دوره 112 شماره
صفحات -
تاریخ انتشار 2012