Planar orientations with low out-degree and compaction of adjacency matrices
نویسندگان
چکیده
منابع مشابه
Planar Orientations with Low Out-degree and Compaction of Adjacency Matrices
We consider the problem of orienting the edges of a planar graph in such a way that the out-degree of each vertex is minimized. If, for each vertex v, the out-degree is at most d, then we say that such an orientation is d-bounded. We prove the following results: • Each planar graph has a 5-bounded acyclic orientation, which can be constructed in linear time. • Each planar graph has a 3-bounded ...
متن کاملLaplacian and the Adjacency Matrices
Proof. We first recall that every non-singular matrix B can be written B = QR, where Q is an orthonormal matrix Q and R is upper-triangular matrix R with positive diagonals1 We will use a slight variation of this fact, writing B = RQ. Now, since QT = Q−1, QAQT has exactly the same eigenvalues as A. Let Rt be the matrix t ∗R+ (1− t)I, and consider the family of matrices Mt = RtQAQR t , as t goes...
متن کاملOn finding orientations with fewest number of vartices with small out-degree
Given an undirected graph, each of the two end-vertices of an edge can “own” the edge. Call a vertex “poor”, if it owns at most one edge. We give a polynomial time algorithm for the problem of finding an assignment of owners to the edges which minimizes the number of poor vertices. In the terminology of graph orientation, this means finding an orientation for the edges of a graph minimizing the...
متن کاملAdjacency Matrices That Are Incidence Matrices: 10967
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive o...
متن کاملAdjacency posets of planar graphs
In this paper, we show that the dimension of the adjacency poset of a planar graph is at most 8. From below, we show that there is a planar graph whose adjacency poset has dimension 5. We then show that the dimension of the adjacency poset of an outerplanar graph is at most 5. From below, we show that there is an outerplanar graph whose adjacency poset has dimension 4. We also show that the dim...
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: Theoretical Computer Science
سال: 1991
ISSN: 0304-3975
DOI: 10.1016/0304-3975(91)90020-3