منابع مشابه
Egalitarian Graph Orientations
Given an undirected graph, one can assign directions to each of the edges of the graph, thus orienting the graph. To be as egalitarian as possible, one may wish to find an orientation such that no vertex is unfairly hit with too many arcs directed into it. We discuss how this objective arises in problems resulting from telecommunications. We give optimal, polynomial-time algorithms for: finding...
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Given an underlying undirected simple graph, we consider the set of all acyclic orientations of its edges. Each of these orientations induces a partial order on the vertices of our graph and, therefore, we can count the number of linear extensions of these posets. We want to know which choice of orientation maximizes the number of linear extensions of the corresponding poset, and this problem w...
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We present a connection between two seemingly disparate fields: VC-theory and graph theory. This connection yields natural correspondences between fundamental concepts in VC-theory, such as shattering and VC-dimension, and well-studied concepts of graph theory related to connectivity, combinatorial optimization, forbidden subgraphs, and others. In one direction, we use this connection to derive...
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Acyclic and cyclic orientations of an undirected graph have been widely studied for their importance: an orientation is acyclic if it assigns a direction to each edge so as to obtain a directed acyclic graph (DAG) with the same vertex set; it is cyclic otherwise. As far as we know, only the enumeration of acyclic orientations has been addressed in the literature. In this paper, we pose the prob...
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ژورنال
عنوان ژورنال: Journal of Graph Algorithms and Applications
سال: 2017
ISSN: 1526-1719
DOI: 10.7155/jgaa.00435