منابع مشابه
Degree Constrained Orientations in Countable Graphs
Degree constrained orientations are orientations of an (undirected) graph where the in-degree function satisfies given lower and upper bounds. For finite graphs Frank and Gyárfás (1976) gave a necessary and sufficient condition for the existence of such an orientation. We extend their result to countable graphs.
متن کاملDegree-Constrained Orientations of Embedded Graphs
We consider the problem of orienting the edges of an embedded graph in such a way that the in-degrees of both the nodes and faces meet given values. We show that the number of feasible solutions is bounded by 22g, where g is the genus of the embedding, and all solutions can be determined within time O(22g|E|2 + |E|3). In particular, for planar graphs the solution is unique if it exists and for ...
متن کاملApproximating Upper Degree-Constrained Partial Orientations
In the Upper Degree-Constrained Partial Orientation problem we are given an undirected graph G = (V,E), together with two degree constraint functions d−, d : V → N. The goal is to orient as many edges as possible, in such a way that for each vertex v ∈ V the number of arcs entering v is at most d−(v), whereas the number of arcs leaving v is at most d(v). This problem was introduced by Gabow [SO...
متن کاملDegree-constrained editing of small-degree graphs
This thesis deals with degree-constrained graph modification problems. In particular, we investigate the computational complexity of DAG Realization and Degree Anonymity. The DAG Realization problem is, given a multiset of positive integer pairs, to decide whether there is a realizing directed acyclic graph (DAG), that is, pairs are one-to-one assigned to vertices such that the indegree and the...
متن کاملMixing Times of Markov Chains on Degree Constrained Orientations of Planar Graphs
We study Markov chains for α-orientations of plane graphs, these are orientations where the outdegree of each vertex is prescribed by the value of a given function α. The set of α-orientations of a plane graph has a natural distrubutive lattice structure. The moves of the up-down Markov chain on this distributive lattice corresponds to reversals of directed facial cycles in the α-orientation. W...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2008
ISSN: 1077-8926
DOI: 10.37236/846