منابع مشابه
Counting the Number of Eulerian Orientations
Consider an undirected Eulerian graph, a graph in which each vertex has even degree. An Eulerian orientation of the graph is an orientation of its edges such that for each vertex v, the number of incoming edges of v equals to outgoing edges of v, i.e. din(v) = dout(v). Let P0 denote the set of all Eulerian orientations of graph G. In this paper, we are concerned with the questions of sampling u...
متن کاملOn the number of planar Eulerian orientations
The number of planar Eulerian maps with n edges is well-known to have a simple expression. But what is the number of planar Eulerian orientations with n edges? This problem appears to be difficult. To approach it, we define and count families of subsets and supersets of planar Eulerian orientations, indexed by an integer k, that converge to the set of all planar Eulerian orientations as k incre...
متن کاملSampling and Counting 3-Orientations of Planar Triangulations
Given a planar triangulation, a 3-orientation is an orientation of the internal edges so all internal vertices have out-degree three. Each 3-orientation gives rise to a unique edge coloring known as a Schnyder wood that has proven powerful for various computing and combinatorics applications. We consider natural Markov chains for sampling uniformly from the set of 3-orientations. First, we stud...
متن کاملReliable Orientations of Eulerian Graphs
We present a characterization of Eulerian graphs that have a k-arc-connected orientation so that the deletion of any vertex results in a (k− 1)-arc-connected directed graph. This provides an affirmative answer for a conjecture of Frank [2]. The special case, when k = 2, describes Eulerian graphs admitting 2-vertexconnected orientations. This case was proved earlier by Berg and Jordán [1]. These...
متن کاملCounting Unique-Sink Orientations
Unique-sink orientations (USOs) are an abstract class of orientations of the ncube graph. We consider some classes of USOs that are of interest in connection with the linear complementarity problem. We summarise old and show new lower and upper bounds on the sizes of some such classes. Furthermore, we provide a characterisation of K-matrices in terms of their corresponding USOs.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2018
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2018.02.040