Cyclically Orientable Graphs
نویسنده
چکیده
Barot, Geiss and Zelevinsky define a notion of a “cyclically orientable graph” and use it to devise a test for whether a cluster algebra is of finite type. Barot, Geiss and Zelivinsky’s work leaves open the question of giving an efficient characterization of cyclically orientable graphs. In this paper, we give a simple recursive description of cyclically orientable graphs, and use this to give an O(n) algorithm to test whether a graph on n vertices is cyclically orientable. Shortly after writing this paper, I learned that most of its results had been obtained independently by Gurvich [2]; I am placing this paper on the arXiv to spread knowledge of these results.
منابع مشابه
On cyclically orientable graphs
Graph G is called cyclically orientable (CO) if it admits an orientation in which every simple chordless cycle is cyclically oriented. This family of graphs was introduced by Barot, Geiss, and Zelevinsky in their paper “Cluster algebras of finite type and positive symmetrizable matrices”, J. London Math. Soc. 73 Part 3 (2006), 545-564. The authors obtained several nice characterizations of CO-g...
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تاریخ انتشار 2005